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

Pages: 193 - 202, Volume 6, Issue 2, May 2012

doi:10.3934/amc.2012.6.193       Abstract        References        Full Text (304.8K)       Related Articles

Suat Karadeniz - Department of Mathematics, Fatih University, 34500, Istanbul, Turkey (email)
Bahattin Yildiz - Department of Mathematics, Fatih University, 34500, Istanbul, Turkey (email)

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 $7$.

Keywords:  Double-circulant, extremal self-dual codes, Gray maps, bordered- double-circulant.
Mathematics Subject Classification:  Primary 94B05, 94B99; Secondary 11T71, 13M99.

Received: April 2011;      Revised: July 2011;      Published: April 2012.

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