2016•AIMS MathematicsOpen access

On deep holes of generalized Reed-Solomon codes

Shaofang Hong, Rongjun Wu

Abstract

Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q-1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. In this paper, we extend this result by giving a new class of deep holes of the generalized Reed-Solomon codes.

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Key concepts: Reed–Solomon error correction, Monomial, Reed–Muller code, Mathematics, Degree (music), Polynomial, Class (philosophy), Combinatorics