Abstract
It is known that it is possible to construct a generator matrix for a self-dual code of length 2n+2 from a generator matrix of a self-dual code of length 2n. With the aid of a computer, we construct new extremal Type I codes of lengths 40, 42, and 44 from extremal self-dual codes of lengths 38, 40, and 42 respectively. Among them are seven extremal Type I codes of length 44 whose weight enumerator is 1+224y 8+872y 10+·. A Type I code of length 44 with this weight enumerator was not known to exist previously.
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Dalan, D.B. New Extremal Type I Codes of Lengths 40, 42, and 44. Designs, Codes and Cryptography 30, 151–157 (2003). https://doi.org/10.1023/A:1025476619824
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DOI: https://doi.org/10.1023/A:1025476619824