DOUBLE-CIRCULANT AND BORDERED-DOUBLE-CIRCULANT CONSTRUCTIONS FOR SELF-DUAL CODES OVER R2.
S Karadeniz, B Yildiz - Advances in Mathematics of …, 2012 - search.ebscohost.com
Advances in Mathematics of communications, 2012•search.ebscohost.com
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< sub> 2= F< sub> 2+
uF< sub> 2+ vF< sub>< sub> 2+ uvF< sub> 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.
circulant constructions for self-dual codes over the non-chain ring R< sub> 2= F< sub> 2+
uF< sub> 2+ vF< sub>< sub> 2+ uvF< sub> 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.
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 R2= F2+ uF2+ vF2+ uvF2 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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