Double-circulant and bordered-double-circulant constructions for self-dual codes over $R_2$

Suat Karadeniz; Bahattin Yildiz

doi:10.3934/amc.2012.6.193

Article Contents

2012, Volume 6, Issue 2: 193-202. Doi: 10.3934/amc.2012.6.193

This issue Previous Article On some classes of constacyclic codes over polynomial residue rings Next Article Good random matrices over finite fields

Double-circulant and bordered-double-circulant constructions for self-dual codes over $R_2$

Suat Karadeniz^1, and
Bahattin Yildiz^1,

1.
Department of Mathematics, Fatih University, 34500, Istanbul

Received: March 31, 2011

Revised: June 30, 2011

Published: April 2012

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Abstract

In this work, the double-circulant, bordered-double-circulant and stripped bordered-double-circulant constructions for self-dual codes over the non-chain ring $R_2 = \mathbb F_2+u\mathbb F_2+v\mathbb F_2+uv\mathbb F_2$ are introduced. Using these methods, we have constructed three extremal binary Type I codes of length $64$ of new weight enumerators for which extremal codes were not known to exist. We also give a double-circulant construction for extremal binary self-dual codes of length $40$ with covering radius $7$.

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Mathematics Subject Classification: Primary 94B05, 94B99; Secondary 11T71, 13M99.

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