A new extension theorem for linear codes

AbstractFor an [n,k,d]q code C with k⩾3, gcd(d,q)=1, the diversity of C is defined as the pair (Φ0,Φ1) withΦ0=1q−1∑q|i,i≠0Ai,Φ1=1q−1∑i≠0,d(modq)Ai.All the diversities for [n,k,d]q codes with k⩾3, d≢−2(modq) such that Ai=0 for all i≢0,−1,−2(modq) are found and characterized with their spectra geometrically, which yields that such codes are extendable for all odd q⩾5. Double extendability is also investigated