Quasi-cyclic dyadic codes in the Walsh-Hadamard transform domain

被引：7

作者：

Rajan, BS ^{[1
]}

Lee, MH

机构：

[1] Indian Inst Sci, Dept Elect Commun Engn, Bangalore 560012, Karnataka, India

[2] Chonbuk Natl Univ, Inst Informat & Commun, Chonju 561756, South Korea

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2002年 / 48卷 / 08期

关键词：

discrete Fourier transform (DFT); dyadic codes; quasicyclic (QC) codes; Walsh-Hadamard transform (WHT);

D O I：

10.1109/TIT.2002.800475

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A code is s-quasi-cyclic (s-QC) if there is an integer s such that cyclic shift of a codeword by s-positions is also a codeword. For s = 1, cyclic codes are obtained. A dyadic code is a code which is closed under all dyadic shifts. An s-QC dyadic (s-QCD) code is one which is both s-QC and dyadic. QCD codes with s = 1 give codes that are cyclic and dyadic (CD). In this correspondence, we obtain a simple characterization of all QCD codes (hence of CD codes) over any field of odd characteristic using Walsh-Hadamard transform defined over that finite field. Also, it is shown that dual a code of an s-QCD code is also an s-OCD code and s-QCD codes for a given dimension are enumerated for all possible values of s.

引用

页码：2406 / 2412

页数：7