Weight Enumerators of Double Circulant Codes and New Extremal Self-Dual Codes |
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| Authors: | T Aaron Gulliver Masaaki Harada |
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| Institution: | (1) Department of Electrical and Electronic Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;(2) Department of Mathematics, Okayama University, Okayama, 700, Japan |
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| 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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| Keywords: | extremal self-dual codes double circulant codes weight enumerators |
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