A new extension theorem for linear codes

For an [n, k, d](q) code 16 with kgreater than or equal to3, gcd(d, q) = 1, the diversity of le is defined as the pair (Phi(0),Phi(1)) with Phi(0) = 1/q-1Sigmaq\i,i not equal0 A(i), Phi = 1/q-1 Sigma(i not equal 0,d (mod q)) A(i). All the diversities for [n, k, d](q) codes with k greater than or equal to 3, d equivalent to -2 (mod q) such that A(i) = 0 for all i not equivalent to 0, -1, -2(mod q) are found and characterized with their spectra geometrically, which yields that such codes are extendable for all odd q greater than or equal to 5Double extendability is also investigated. (C) 2004 Elsevier Inc. All rights reserved.