Rajan, B. S. ; Ho Lee, Moon (2002) Quasi-cyclic dyadic codes in the Walsh-Hadamard transform domain IEEE Transactions on Information Theory, 48 (8). pp. 2406-2412. ISSN 0018-9448
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Official URL: http://ieeexplore.ieee.org/document/1019853/
Related URL: http://dx.doi.org/10.1109/TIT.2002.800475
Abstract
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). 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-QCD code and s-QCD codes for a given dimension are enumerated for all possible values of s.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Electrical and Electronics Engineers. |
| ID Code: | 107998 |
| Deposited On: | 08 Dec 2017 10:13 |
| Last Modified: | 08 Dec 2017 10:13 |
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