In 1940, Ulam 1 gave a wide ranging talk before the mathematics club of the University of Wisconsin in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms: “Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 satisfies...

Our purpose is to find an upper bound for the length of s-extremal codes over F2 (resp. F4) when d ≡ 2 (mod 4) (resp. d odd). This question is left open in [6], [2]. More precisely, we show that there is no s-extremal binary code of length n ≥ 21d− 82 if d > 6 and d ≡ 2 (mod 4). Similarly we show that there is no s-extremal additive F4 code of length n ≥ 13d− 26 if d > 1 and d is odd. We also d...