MDS and near-mds self-dual codes over large prime fields

Kotsireas, IS; Koukouvinos, C; Simos, DE

dc.contributor.author	Kotsireas, IS	en
dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Simos, DE	en
dc.date.accessioned	2014-03-01T01:31:03Z
dc.date.available	2014-03-01T01:31:03Z
dc.date.issued	2009	en
dc.identifier.issn	1930-5346	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19725
dc.subject	Circulant matrices	en
dc.subject	Construction	en
dc.subject	Diophantine equations	en
dc.subject	MDS codes	en
dc.subject	NMDS codes	en
dc.subject	Self-dual codes	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	COMBINATORIAL DESIGNS	en
dc.subject.other	CLASSICAL ARCS	en
dc.subject.other	GF(7)	en
dc.subject.other	PG(R,Q)	en
dc.title	MDS and near-mds self-dual codes over large prime fields	en
heal.type	journalArticle	en
heal.identifier.primary	10.3934/amc.2009.3.349	en
heal.identifier.secondary	http://dx.doi.org/10.3934/amc.2009.3.349	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In this paper, we are interested in the construction of maximum distance separable (MDS) self-dual codes over large prime fields that arise from the solutions of systems of diophantine equations. Using this method we con-struct many self-dualMDS (or near-MDS) codes of lengths up to 16 over various prime fields GF(p), where p = 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193 and 197. In addition, a number of optimal codes are presented for many lengths up to 40 over small prime fields GF(p). Furthermore, our results on the minimum weight of self-dual codes over prime fields give a better bound than the Pless-Pierce bound obtained from a modified Gilbert-Varshamov bound. © 2009 AIMS-SDU.	en
heal.publisher	AMER INST MATHEMATICAL SCIENCES	en
heal.journalName	Advances in Mathematics of Communications	en
dc.identifier.doi	10.3934/amc.2009.3.349	en
dc.identifier.isi	ISI:000273229300004	en
dc.identifier.volume	3	en
dc.identifier.issue	4	en
dc.identifier.spage	349	en
dc.identifier.epage	361	en