SQUARE ELEMENTS IN GALOIS RINGS AND MDS SELF-DUAL CODES

SQUARE ELEMENTS IN GALOIS RINGS AND MDS SELF-DUAL CODES

Let GR(2^m, r) be a Galois ring with even characteristic. We prove that if r is even and n ≡ 0 (mod 4), then -(n-1) is a square element in GR(2^m, r) for all m ≥ 1. Using this fact we also prove that if (n - 1) | (2^r - 1), 4 | n, and r is even, then there exists an MDS(Maximum Distance Separable) self-dual code over GR(2^m, r) with parameters [n, n/2, n/2+ 1].

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