On the extendability of quaternary linear codes with four weights modulo 16

We consider the extendability of linear codes over the field of order 4 whose codewords have at most four weights modulo 16. For instance, we prove that every [n, k, d]4 code with d --3 (mod 16), k > 3, is extendable if all possible weights of codewords are congruent to 0, -1, -2, -3 (mod 16). Such a code with d --1 or -2 (mod 16) is extendable as well except for some cases.(c) 2022 Elsevier B.V. All rights reserved.