Upper Bounds for the Lengths of $s$-Extremal Codes Over $\BBF _{2}$, $\BBF _{4}$, and $\BBF _{2} + u\BBF _{2}$
Sunghyu Han, Jon-Lark Kim · IEEE Transactions on Information Theory · 2008
Our purpose is to find an upper bound for the length of ans-extremal code over F2(resp. F4) when d equiv 2 (mod 4) (resp. d odd). This question is left open in [A bound for certain s -extremal lattices and codes, Archiv der Mathematik, vol. 89, no. 2, pp. 143-151, 2007] (resp. [s-extremal additive F4codes, Advances in Mathematics of Communications, vol. 1, no. 1, pp. 111-130,2007]). More precisely, we show that if there is an [n, n/2, d]s-extremal Type I binary self-dual code with d > 6 and d equiv 2 (mod 4), then n1 and d, equiv 1 (mod 2), then n2+ uF2and derive an upper bound for the length of an .s-extremal self-dual code over F2+ uF2using the information on binarys-extremal codes.