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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)

- MIHAI CARAGIU
- 2001

We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P (X,Y) ∈ GF (q)[X, Y ] with coefficients in the finite field GF (q) with q elements, with prescribed level curves X c := {(x, y) ∈ GF (q) 2 | P (x,y) = c}. 1. Introduction. Let GF (q) be the finite field with q elements. Assume that for any c ∈ GF… (More)

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