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Self-dual codes using the building-up construction

The building-up construction for self-dual codes was developed by the authors over finite fields GF(q) when q is a power of 2 or q ≡ 1 (mod 4). In this paper, we complete the building-up construction for self-dual codes over GF(q) with q ≡ 3 (mod 4). For example, we construct new 945 extremal self-dual ternary [32, 16, 9] codes, each of which has a trivial automorphism group.