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.
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页码：2406 / 2412
页数：7
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