TY - JOUR
T1 - Weight Enumerators of Double Circulant Codes and New Extremal Self-Dual Codes
AU - Gulliver, T. Aaron
AU - Harada, Masaaki
PY - 1997
Y1 - 1997
N2 - 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.
AB - 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.
KW - Double circulant codes
KW - Extremal self-dual codes
KW - Weight enumerators
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U2 - 10.1023/A:1008276604233
DO - 10.1023/A:1008276604233
M3 - Article
AN - SCOPUS:0042070281
SN - 0925-1022
VL - 11
SP - 141
EP - 150
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 2
ER -