Abstract
In this paper, we give a pseudo-random method to construct extremal Type II codes overℤ4 . As an application, we give a number of new extremal Type II codes of lengths 24, 32 and 40, constructed from some extremal doubly-even self-dual binary codes. The extremal Type II codes of length 24 have the property that the supports of the codewords of Hamming weight 10 form 5−(24,10,36) designs. It is also shown that every extremal doubly-even self-dual binary code of length 32 can be considered as the residual code of an extremal Type II code over ℤ4.
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Gaborit, P., Harada, M. Construction of Extremal Type II Codes over ℤ4 . Designs, Codes and Cryptography 16, 257–269 (1999). https://doi.org/10.1023/A:1008335912135
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DOI: https://doi.org/10.1023/A:1008335912135