On Designs and Formally Self-Dual Codes
George T. Kennedy, Vera S. Pless · 2005
Binary formally self-dual (f.s.d) even codes are the one type of divisible [2n, n] codes which need not be self-dual. 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 Assrnm-Mattson theorem. If C is a f.s. d. extremal code of length n= 2 (mod 8)[n=6 (mod 8)], then the words of a fixed weight in CUC1 hold a 3-design [1-design]. FinalIy, we show that the extremal f.s. d. codes of lengths 10 and 18 are unique.