An extension theorem for [n, k, d]d codes with gcd(d, q)=2

As a continuation of Maruta [Finite Fields Appl. 10 (2004), 674–685], we investigate the extendability of [n, k, d]q codes with d ≡ −2 (mod q) whose weights are congruent to 0, −1 or −2 (mod q) for even q ≥ 4. We show that such codes are extendable for all even q ≥ 8, giving a new extension theorem for [n, k, d]q codes with gcd(d, q) = 2. We also consider the extendability of such codes for q = 4.