Some results on linear subspace codes

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-02-14 DOI:10.1016/j.ffa.2025.102596

Mahak, Maheshanand Bhaintwal

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引用次数: 0

Abstract

The notion of linearity in projective spaces was defined by Etzion and Vardy (2008) [3]. In this paper, we have obtained some results on linear subspace codes. We have proved that if in a linear subspace code C in the projective space

P_{q} (n)

, the number of one-dimensional subspaces is

n - 1

, then the cardinality of C is

2^{n - 1}

; and if the number of the one-dimensional subspaces in C is

n - 2

and the ambient space does not belong to C, then the cardinality of C is

2^{n - 2}

. We have also studied complementary linear subspace codes. An example has been given to show that a complement function can exist on a non-distributive sublattice of the projective lattice. We have also proved that a non-distributive sublattice of the projective lattice cannot be a linear subspace code.

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关于线性子空间码的一些结果

投影空间中的线性概念是由Etzion和Vardy（2008）定义的。在本文中，我们得到了关于线性子空间码的一些结果。证明了如果在射影空间Pq(n)中的线性子空间编码C中，一维子空间的个数为n−1，则C的基数为2n−1；若C中的一维子空间个数为n−2，且周围空间不属于C，则C的基数为2n−2。我们也研究了互补线性子空间码。给出了一个例子，证明了补函数可以存在于射影格的非分配子格上。并证明了射影格的非分配子格不可能是线性子空间码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.