LCD codes from tridiagonal Toeplitz matrices

被引：54

作者：

Shi, Minjia ^{[1
]}

Ozbudak, Ferruh ^{[2
,3
]}

Xu, Li ^{[4
]}

Sole, Patrick ^{[5
]}

机构：

[1] Anhui Univ, Sch Math Sci, Key Lab Intelligent Comp Signal Proc, Minist Educ, Hefei 230601, Anhui, Peoples R China

[2] Middle East Tech Univ, Dept Math, Ankara, Turkey

[3] Middle East Tech Univ, Inst Appl Math, Ankara, Turkey

[4] Anhui Univ, Sch Math Sci, Hefei 230601, Anhui, Peoples R China

[5] Aix Marseille Univ, Cent Marseille, CNRS, Aix En Provence, France

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2021年 / 75卷

基金：

中国国家自然科学基金;

关键词：

LCD codes; Toeplitz matrices; Dickson polynomials; LINEAR CODES; EQUIVALENT;

D O I：

10.1016/j.ffa.2021.101892

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Double Toeplitz (DT) codes are codes with a generator matrix of the form (I, T) with T a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When T is tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, and deduce from there conditions for the code to be LCD. Using a special concatenation process, we construct optimal or quasi-optimal examples of binary and ternary LCD codes from DT codes over extension fields. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：17

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