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Polynomials generating Hamming codes

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A class of polynomials generatingq-nary Hamming codes is studied. The criteria for a polynomial to belong to this class are established for the general case and for the case of prime polynomials. The conditions are determined under which reducible polynomials do not belong to the class of polynomials generating theq-nary Hamming codes.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 893–897, July, 1993.

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Barashko, A.S. Polynomials generating Hamming codes. Ukr Math J 45, 987–992 (1993). https://doi.org/10.1007/BF01057445

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  • Reducible Polynomial
  • Prime Polynomial