Journal Name:
- European Journal of Pure and Applied Mathematics
Author Name | University of Author |
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Abstract (2. Language):
We study self-dual codes over an infinite family of rings, denoted Rk, which has been recently
introduced to the literature. We prove that for each self-dual code over Rk, k ≥ 2, there exist a
corresponding binary self-dual code, a real unimodular lattice, a complex unimodular lattice, a quaternionic
lattice and an infinite family of self-dual codes. We prove the existence of Type II codes of all
lengths over Rk, for k ≥ 3, and we obtain some extremal binary self-dual codes including the extended
binary Golay code as the Gray images of self-dual codes over Rk for some suitable k. The binary
self-dual codes obtained from Rk all have automorphism groups whose orders are a multiple of 2k.
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FULL TEXT (PDF):
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