An application of bivariate polynomial factorization on decoding of Reed-Solomon based codes | Zendy

Ivan Pavkov | Zendy; Nebojša Ralević | Zendy; Ljubo Nedović | Zendy

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An application of bivariate polynomial factorization on decoding of Reed-Solomon based codes

Author(s) -

Ivan Pavkov,

Nebojša Ralević,

Ljubo Nedović

Publication year - 2017

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm170530005p

Subject(s) - mathematics , bivariate analysis , factorization , factorization of polynomials , polynomial , integer (computer science) , decoding methods , code word , factoring , discrete mathematics , combinatorics , square free polynomial , irreducible polynomial , matrix polynomial , algorithm , statistics , mathematical analysis , finance , computer science , economics , programming language

A necessary and sufficient condition for the existence of a non-trivial factorization of an arbitrary bivariate polynomial with integer coefficients was presented in [2]. In this paper we develop an efficient algorithm for factoring bivariate polynomials with integer coefficients. Also, we shall give a proof of the optimality of the algorithm. For a given codeword, formed by mixing up two codewords, the algorithm recovers those codewords directly by factoring corresponding bivariate polynomial. Our algorithm determines uniquely the given polynomials which are used in forming the mixture of two codewords.

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