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For any odd prime power q we first construct a certain non-linear binary code C(q, 2) having (q 2 − q)/2 codewords of length q and weight (q − 1)/2 each, for which the Hamming distance between any two distinct codewords is in the range [q/2 − 3 √ q/2, q/2 + 3 √ q/2] that is, 'almost constant'. Moreover, we prove that C(q, 2) is distance-invariant. Several… (More)

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