On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots

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• 作者：San Ling ; Harald Niederreiter and Patrick Sol¨¦
• 关键词：quasi ; cyclic codes ; GDFT ; Hasse derivative ; codes over rings ; self ; dual codes ; Type II codes
• 刊名：Designs, Codes and Cryptography
• 出版年：2006
• 出版时间：March 2006
• 年：2006
• 卷：38
• 期：3
• 页码：337-361
• 全文大小：234 KB

文摘

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.