A class of t-weight codes and its applications

Pub Date : 2023-11-03 DOI:10.1142/s0219498825500963
J. Prabu, J. Mahalakshmi, S. Santhakumar
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Abstract

In this paper, we constructed a class of [Formula: see text]-weight linear codes over [Formula: see text] under the homogeneous weight metric by their generator matrices, where [Formula: see text] and [Formula: see text] The Gray images of some class of these codes over [Formula: see text] are [Formula: see text]-ary nonlinear codes, which have the same weight distributions as that of the two-weight [Formula: see text]-ary linear codes of type SU1 in the sense of [R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18(2) (1986) 97–122]. Also, we obtained the minimum distance of the dual codes of the constructed codes. Further, we discussed some optimal linear codes over [Formula: see text] with respect to Plotkin-type bound from the constructed codes when [Formula: see text] Furthermore, we investigated the applications in strongly regular graphs and secret sharing schemes.
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一类t权码及其应用
本文通过生成矩阵在齐次权测度下构造了一类[公式:见文]上的[公式:见文]-权线性码,其中[公式:见文]和[公式:见文]这类码在[公式:见文]上的灰度图像为[公式:见文]-任意非线性码,其权重分布与[R]意义上的双权[公式:见文]-任意线性码的权重分布相同。卡尔德班克和W. M.坎特,二权码的几何性质,第2卷。伦敦数学。Soc. 18(2)(1986) 97-122]。同时,我们得到了所构造码的对偶码的最小距离。在此基础上,我们进一步讨论了[公式:见文]构造的码在[公式:见文]上关于plotkin型界的一些最优线性码,并研究了它们在强正则图和秘密共享方案中的应用。
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