Linear codes associated to symmetric determinantal varieties: Even rank case

被引：2
|
作者：
Beelen, Peter [1 ]
Johnsen, Trygve [2 ]
Singh, Prasant [3 ]
机构：
[1] Tech Univ Denmark, Dept Appl Math & Comp Sci, Matematiktorvet 303B, DK-2800 Lyngby, Denmark
[2] UiT Arctic Univ Norway, Dept Math & Stat, Hansine Hansens Veg 18, N-9019 Tromso, Norway
[3] IIT Jammu, Dept Math, Srinagar 181221, Jammu & Kashmir, India
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2023年 / 91卷
关键词：
Symmetric determinantal varieties; Symmetric matrices; Linear code; Minimum distance;
D O I：
10.1016/j.ffa.2023.102240
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider linear codes over a finite field Fq, for odd q, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a codeword is derived. Using this formula, we have computed the minimum distance for the codes corresponding to matrices upperbounded by any fixed, even rank. A conjecture is proposed for the cases where the upper bound is odd. At the end of the article, tables for the weights of these codes, for spaces of symmetric matrices up to order 5, are given.& COPY; 2023 Elsevier Inc. All rights reserved.
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