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New databases of linear codes over GF(11) and GF(13)
Högskolan Kristianstad, Sektionen för hälsa och samhälle, Avdelningen för Design och datavetenskap. (Computer Science)
USA.
2014 (engelsk)Inngår i: Proceedings of Karatekin mathematics days 2014: international mathematics symposium, 2014, s. 22-22Konferansepaper, Oral presentation with published abstract (Fagfellevurdert)
Abstract [en]

One central problem in coding theory is to optimize the parameters of a linear code and construct codes with best possible parameters. There are tables of best-known linear codes over nite elds of sizes up to 9. Recently, there has been a growing interest in codes over GF(11), over GF(13) and other elds of size greater than 9. The main purpose of this work is to present new databases of best-known linear codes over the elds GF(11) and GF(13) together with upper bounds on the minimum distances. To nd good linear codes to establish lower bounds on minimum distances, an iterative heuristic computer search algorithm is employed to construct quasi-twisted (QT) codes over these elds with high minimum distances. A large number of new linear codes have been found, improving previously best-known results. Tables of [pm, m] QT codes over the two elds with best-known minimum distances as well as a table of lower and upper bounds on the minimum distances for linear codes of length up to 150 and dimension up to 6 are presented.

sted, utgiver, år, opplag, sider
2014. s. 22-22
Emneord [en]
Database of linear codes, quasi-twisted codes, heuristic search algorithm, iterative search
HSV kategori
Identifikatorer
URN: urn:nbn:se:hkr:diva-14835OAI: oai:DiVA.org:hkr-14835DiVA, id: diva2:857324
Konferanse
Karatekin Mathematics Days 2014, Çankırı, Turkey, 11-13 June, 2014
Tilgjengelig fra: 2015-09-28 Laget: 2015-09-28 Sist oppdatert: 2018-01-11bibliografisk kontrollert

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