Abstract
Binary formally self-dual (f.s.d.) even codes are the one type of divisible [2n, n] codes which need not be self-dual. We examine such codes in this paper. On occasion a f.s.d. even [2n, n] code can have a larger minimum distance than a [2n, n] self-dual code. We give many examples of interesting f.s.d even codes. We also obtain a strengthening of the Assmus-Mattson theore. IfC is a f.s.d. extremal code of lengthn≡2 (mol 8) [n ≡6 (mod 8)], then the words of a fixed weight inC ∪C ⊥ hold a 3-design [1-design]. Finally, we show that the extremal f.s.d. codes of lengths 10 and 18 are unique.
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Communicated by S. Vanstone
The author thanks the University of Illinois at Chicago for their hospitality while this work was in progress.
This work was supported in part by NSA Grant MDA 904-91-H-0003.
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Kennedy, G.T., Pless, V. On designs and formally self-dual codes. Des Codes Crypt 4, 43–55 (1994). https://doi.org/10.1007/BF01388559
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DOI: https://doi.org/10.1007/BF01388559