On the Residue Codes of Extremal Type II Z4-Codes of Lengths 32 and 40

Details On the Residue Codes of Extremal Type II Z4-Codes of Lengths 32 and 40 On the Residue Codes of Extremal Type II Z4-Codes of Lengths 32 and 40

2011-04-20

arxiv.org/abs/1104.3925v1

Mathematics

Combinatorics

19 pages

Scientific paper

In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes for lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some extremal Type II Z4-code. It is also shown that there is a unique extremal Type II Z4-code of length 32 whose residue code has the smallest dimension 6 up to equivalence. As a consequence, many new extremal Type II Z4-codes of lengths 32 and 40 are constructed.

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