Generators and weights of polynomial codes
نویسنده
چکیده
Introduction. Several authors have established that many classical codes are ideals in certain ring constructions. Berman [3], in the case of characteristic two, and Charpin [5], in the general case, proved that all generalized Reed-Muller codes coincide with powers of the radical of the quotient ring A = Fq[x1, . . . , xn]/(x q1 1 − 1, . . . , xn n − 1), where Fq is a finite field, p = charFq > 0 and qi = p ci , for i = 1, . . . , n, and gave formulas for their Hamming weights. These codes form an important class containing many codes of practical value. Properties of error-correcting codes in similar ring constructions A have also been considered by Poli [12].
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