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On existence of good self-dual quasicyclic codes

DSpace at IIT Bombay

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Title On existence of good self-dual quasicyclic codes
 
Creator DEY, BK
 
Subject binary codes
cyclic codes
discrete fourier transforms
dual codes
 
Description For a long time, asymptotically good self-dual codes have been known to exist. Asymptotically good 2-quasicyclic codes of rate 1/2 have also been known to exist for a long time. Recently, it was proved that there are binary self-dual n/3-quasicyclic codes of length n asymptotically meeting the Gilbert-Varshamov bound. Unlike 2-quasicyclic codes, which are defined to have a cyclic group of order n/2 as a subgroup of their permutation group, the n/3-quasicyclic c codes are defined with a permutation group of fixed order of 3. So, from the decoding point of view, 2-quasicyclic c codes are preferable to n/3-quasicyclic c codes. In this correspondence, with the assumption that there are infinite primes p with respect to (w r t.) which 2 is primitive, we prove that there exist classes of self-dual 2p-quasicyclic c codes and Type II 8p-quasicyclic c codes of length respectively 2p2 and 8p2 which asymptotically meet the Gilbert-Varshamov bound. When compared with the order of the defining permutation groups, these classes of codes lie between the 2-quasicyclic c codes and the n/3-quasicyclic c codes of length n, considered in previous works.
 
Publisher IEEE
 
Date 2009-01-05T03:28:48Z
2011-11-25T16:23:19Z
2011-12-26T13:05:26Z
2011-12-27T05:52:23Z
2009-01-05T03:28:48Z
2011-11-25T16:23:19Z
2011-12-26T13:05:26Z
2011-12-27T05:52:23Z
2004
 
Type Article
 
Identifier IEEE Transactions on Information Theory 50 (8), 1794-1798
0018-9448
http://hdl.handle.net/10054/535
http://dx.doi.org/10.1109/TIT.2004.831855
http://dspace.library.iitb.ac.in/xmlui/handle/10054/535
 
Language en