Abstract
All singly-even self-dual [40,20,8] binary codes which have an automorphism of prime order \(p \geqslant 5\) are obtained up to equivalence. There are two inequivalent codes with an automorphism of order 7 and 37 inequivalent codes with an automorphism of order 5. These codes have highest possible minimal distance and some of them are the first known codes with weight enumerators prescribed by Conway and Sloane.
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Buyuklieva, S., Yorgov, V. Singly-Even Self-Dual Codes of Length 40. Designs, Codes and Cryptography 9, 131–141 (1996). https://doi.org/10.1023/A:1018057829391
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DOI: https://doi.org/10.1023/A:1018057829391