IEEE Transactions on Information Theory最新文献

{"title":"Combinatorial Constructions of Optimal Quaternary Additive Codes","authors":"Chaofeng Guan;Jingjie Lv;Gaojun Luo;Zhi Ma","doi":"10.1109/TIT.2024.3467123","DOIUrl":"https://doi.org/10.1109/TIT.2024.3467123","url":null,"abstract":"This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive \u0000<inline-formula> <tex-math>$[n,3.5,n-t]_{4}$ </tex-math></inline-formula>\u0000 codes for all t with variable n, except for \u0000<inline-formula> <tex-math>$t=6,7,12$ </tex-math></inline-formula>\u0000.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7690-7700"},"PeriodicalIF":2.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two New Classes of MDS Symbol-Pair Codes","authors":"Xiaoshan Kai;Yajing Zhou;Shixin Zhu","doi":"10.1109/TIT.2024.3466523","DOIUrl":"https://doi.org/10.1109/TIT.2024.3466523","url":null,"abstract":"Due to the application of high density data storage systems, symbol-pair codes are proposed to combat errors of the overlapping symbol pairs output over symbol-pair read channels. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they have the highest pair error-correcting capability. In this paper, we construct two new classes of MDS symbol-pair codes with minimum pair distance seven based on simple-root cyclic codes. Our technique is through the decomposition of cyclic codes and the dual of each component code.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7701-7710"},"PeriodicalIF":2.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142517997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spherical Codes With Prescribed Signed Permutation Automorphisms Inside Shells of Low-Dimensional Integer Lattices","authors":"Mikhail Ganzhinov;Patric R. J. Östergård","doi":"10.1109/TIT.2024.3462593","DOIUrl":"https://doi.org/10.1109/TIT.2024.3462593","url":null,"abstract":"Let \u0000<inline-formula> <tex-math>$textrm {S}(n,t,k)$ </tex-math></inline-formula>\u0000 be the maximum size of a code containing only vectors of the kth shell of the integer lattice \u0000<inline-formula> <tex-math>$mathbb {Z}^{n}$ </tex-math></inline-formula>\u0000 such that the inner product between distinct vectors does not exceed t. In this paper we compute lower bounds for \u0000<inline-formula> <tex-math>$textrm {S}(n,t,k)$ </tex-math></inline-formula>\u0000 for small values of n, t and k by carrying out computer searches for codes with prescribed automorphisms. We prescribe groups of signed permutation automorphisms acting transitively on the pairs of coordinates and coordinate values as well as other closely related groups of automorphisms. Several of the constructed codes lead to improved lower bounds for spherical codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8669-8674"},"PeriodicalIF":2.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10688409","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two Classes of Constacyclic Codes With a Square-Root-Like Lower Bound","authors":"Tingfang Chen;Zhonghua Sun;Conghui Xie;Hao Chen;Cunsheng Ding","doi":"10.1109/TIT.2024.3464630","DOIUrl":"https://doi.org/10.1109/TIT.2024.3464630","url":null,"abstract":"Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In this paper, an infinite class of q-ary negacyclic codes of length \u0000<inline-formula> <tex-math>$(q^{m}-1)/2$ </tex-math></inline-formula>\u0000 and an infinite class of q-ary constacyclic codes of length \u0000<inline-formula> <tex-math>$(q^{m}-1)/(q-1)$ </tex-math></inline-formula>\u0000 are constructed and analyzed. As a by-product, two infinite classes of ternary negacyclic self-dual codes with a square-root-like lower bound on their minimum distances are presented.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8734-8745"},"PeriodicalIF":2.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Consistent Estimation of a Class of Distances Between Covariance Matrices","authors":"Roberto Pereira;Xavier Mestre;David Gregoratti","doi":"10.1109/TIT.2024.3464678","DOIUrl":"https://doi.org/10.1109/TIT.2024.3464678","url":null,"abstract":"This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. This family of distances is particularly useful as it takes into consideration the fact that covariance matrices lie in the Riemannian manifold of positive definite matrices, thereby including a variety of commonly used metrics, such as the Euclidean distance, Jeffreys’ divergence, and the log-Euclidean distance. Moreover, a statistical analysis of the asymptotic behavior of this class of distance estimators has also been conducted. Specifically, we present a central limit theorem that establishes the asymptotic Gaussianity of these estimators and provides closed form expressions for the corresponding means and variances. Empirical evaluations demonstrate the superiority of our proposed consistent estimator over conventional plug-in estimators in multivariate analytical contexts. Additionally, the central limit theorem derived in this study provides a robust statistical framework to assess of accuracy of these estimators.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"8107-8132"},"PeriodicalIF":2.2,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes","authors":"Amit Berman;Yaron Shany;Itzhak Tamo","doi":"10.1109/TIT.2024.3465218","DOIUrl":"https://doi.org/10.1109/TIT.2024.3465218","url":null,"abstract":"We present \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$O(m^{3})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 algorithms for specifying the support of minimum-weight codewords of extended binary BCH codes of length \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$n=2^{m}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 and designed distance \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$d(m,s,i):=2^{m-1-s}-2^{m-1-i-s}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 for some values of \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$m,i,s$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, where m may grow to infinity. Here, the support is specified as the sum of two sets: a set of \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$2^{2i-1}-2^{i-1}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 elements, and a subspace of dimension \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$m-2i-s$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, specified by a basis. In some detail, for designed distance \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$6cdot 2^{j}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$jin {0,ldots ,m-4}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, we have a deterministic algorithm for even \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$mgeq 4$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, and a probabilistic algorithm with success probability \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$1-O(2^{-m})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 for odd \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$mgt 4$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000. For designed distance \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$28cdot 2^{j}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$jin {0,ldots , m-6}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, we have a probabilistic algorithm with success probability \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$geq frac {1}{3}-O(2^{-m/2})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 for even \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$mgeq 6$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000. Finally, for designed distance \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$120cdot 2^{j}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$jin {0,ldots , m-8}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, we have a deterministic algorithm for \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$mgeq 8$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 divisible by 4. We also show how Gold functions can be used to find the support of minimum-weight words for designed distance \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$d(m,s,i)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 (for \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$iin {0,ldots ,lfloor m/2rfloor }$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, and \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$sleq m-2i$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000) whenever \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$2i|m$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000. Our construction builds on results of Kasami and Lin, who proved that for extended binary BCH codes of designed distance \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$d(m,s,i)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 (for integers \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$mgeq 2$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$0leq ileq lfloor m/2rfloor $ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, and \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$0leq sleq m-2i$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000), the minimum distance equals the designed distance. The proof of Kasami and Lin makes use of a non-constructive existence result of Berlekamp, and a constructive “dow","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7673-7689"},"PeriodicalIF":2.2,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142517943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Support Recovery in Mixture Models with Sparse Parameters","authors":"Arya Mazumdar, Soumyabrata Pal","doi":"10.1109/tit.2024.3462937","DOIUrl":"https://doi.org/10.1109/tit.2024.3462937","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"17 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2024.3455151","DOIUrl":"https://doi.org/10.1109/TIT.2024.3455151","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"C3-C3"},"PeriodicalIF":2.2,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10682503","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generator Polynomials of Cyclic Expurgated or Extended Goppa Codes","authors":"Xue Jia;Fengwei Li;Huan Sun;Qin Yue","doi":"10.1109/TIT.2024.3462712","DOIUrl":"10.1109/TIT.2024.3462712","url":null,"abstract":"Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic parity-check subcode. Let \u0000<inline-formula> <tex-math>$Bbb F_{q}$ </tex-math></inline-formula>\u0000 be a finite field with \u0000<inline-formula> <tex-math>$q=2^{l}$ </tex-math></inline-formula>\u0000 elements, where l is a positive integer. In this paper, we determine all the generator polynomials of cyclic expurgated or extended Goppa codes under some prescribed permutations induced by the projective general linear automorphism \u0000<inline-formula> <tex-math>$A in PGL_{2}(Bbb F_{q})$ </tex-math></inline-formula>\u0000. Moreover, we provide some examples to support our findings.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7711-7722"},"PeriodicalIF":2.2,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IEEE Transactions on Information Theory Publication Information","authors":"","doi":"10.1109/TIT.2024.3455153","DOIUrl":"10.1109/TIT.2024.3455153","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"C2-C2"},"PeriodicalIF":2.2,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10682504","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}