Self-orthogonal and self-dual codes constructed via combinatorial designs and diophantine equations

Georgiou, S; Koukouvinos, C

dc.contributor.author	Georgiou, S	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T02:42:58Z
dc.date.available	2014-03-01T02:42:58Z
dc.date.issued	2004	en
dc.identifier.issn	0925-1022	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/31155
dc.subject	Construction	en
dc.subject	Diophantine equations	en
dc.subject	Generalized orthogonal designs	en
dc.subject	Self-dual codes	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Codes (symbols)	en
dc.subject.other	Construction	en
dc.subject.other	Cryptography	en
dc.subject.other	Logic design	en
dc.subject.other	Mathematical models	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Vectors	en
dc.subject.other	Diophantine equations	en
dc.subject.other	Generalized orthogonal designs	en
dc.subject.other	Self-dual codes	en
dc.subject.other	Combinatorial mathematics	en
dc.title	Self-orthogonal and self-dual codes constructed via combinatorial designs and diophantine equations	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1023/B:DESI.0000029222.35938.bf	en
heal.identifier.secondary	http://dx.doi.org/10.1023/B:DESI.0000029222.35938.bf	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	Combinatorial designs have been widely used, in the construction of self-dual codes. Recently, new methods of constructing self-dual codes are established using orthogonal designs (ODs), generalized orthogonal designs (GODs), a set of four sequences and Diophantine equations over GF(p). These methods had led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we used some methods to construct self-orthogonal and self dual codes over GF(p), for some primes p. The construction is achieved by using some special kinds of combinatorial designs like orthogonal designs and GODs. Moreover, we combine eight circulant matrices, a system of Diophantine equations over GF(p), and a recently discovered array to obtain a new construction method. Using this method new self-dual and self-orthogonal codes are obtained. Specifically, we obtain new self-dual codes [32; 16; 12] over GF(11) and GF(13) which improve the previously known distances.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	Designs, Codes, and Cryptography	en
dc.identifier.doi	10.1023/B:DESI.0000029222.35938.bf	en
dc.identifier.isi	ISI:000221666000015	en
dc.identifier.volume	32	en
dc.identifier.issue	1-3	en
dc.identifier.spage	193	en
dc.identifier.epage	206	en