Weight enumerators of double circulant codes and new extremal self-dual codes
TA Gulliver, M Harada - Designs, Codes and Cryptography, 1997 - Springer
Designs, Codes and Cryptography, 1997•Springer
In this paper it is shown that the weight enumerator of a bordered double circulant self-dual
code can be obtained from those of a pure double circulant self-dual code and its shadow
through a relationship between bordered and pure double circulant codes. As applications,
a restriction on the weight enumerators of some extremal double circulant codes is
determined and a uniqueness proof of extremal double circulant self-dual codes of length 46
is given. New extremal singly-even [44, 22, 8] double circulant codes are constructed. These …
code can be obtained from those of a pure double circulant self-dual code and its shadow
through a relationship between bordered and pure double circulant codes. As applications,
a restriction on the weight enumerators of some extremal double circulant codes is
determined and a uniqueness proof of extremal double circulant self-dual codes of length 46
is given. New extremal singly-even [44, 22, 8] double circulant codes are constructed. These …
Abstract
In this paper it is shown that the weight enumerator of a bordered double circulant self-dual code can be obtained from those of a pure double circulant self-dual code and its shadow through a relationship between bordered and pure double circulant codes. As applications, a restriction on the weight enumerators of some extremal double circulant codes is determined and a uniqueness proof of extremal double circulant self-dual codes of length 46 is given. New extremal singly-even [44,22,8] double circulant codes are constructed. These codes have weight enumerators for which extremal codes were not previously known to exist.
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