On the algebraic structure of quasi-cyclic codes IV:: Repeated roots

被引：37

作者：

Ling, S ^{[1
]}

Niederreiter, H

Solé, P

机构：

[1] Nanyang Technol Univ, Sch Math & Phys Sci, Div Math Sci, Singapore 637616, Singapore

[2] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

[3] ESSI, CNRS, F-06903 Sophia Antipolis, France

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2006年 / 38卷 / 03期

关键词：

quasi-cyclic codes; GDFT; Hasse derivative; codes over rings; self-dual codes; Type II codes;

D O I：

10.1007/s10623-005-1431-7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A trace formula for quasi-cyclic codes over rings of characteristic not coprime with the co-index is derived. The main working tool is the Generalized Discrete Fourier Transform (GDFT), which in turn relies on the Hasse derivative of polynomials. A characterization of Type II self-dual quasi-cyclic codes of singly even co-index over finite fields of even characteristic follows. Implications for generator theory are shown. Explicit expressions for the combinatorial duocubic, duoquintic and duoseptic constructions in characteristic two over finite fields are given.

引用

页码：337 / 361

页数：25

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