In this paper, we consider the affine variety codes obtained evaluating the polynomials by = a(k)(xk) + ... + a(1)x + a(0), b, a(i) is an element of F-qr, at the affine F-qr-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolute irreducibility of certain algebraic varieties.
Minimal codewords in Norm-Trace codes
Bartoli, Daniele;Timpanella, Marco
2024
Abstract
In this paper, we consider the affine variety codes obtained evaluating the polynomials by = a(k)(xk) + ... + a(1)x + a(0), b, a(i) is an element of F-qr, at the affine F-qr-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolute irreducibility of certain algebraic varieties.File in questo prodotto:
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