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On deep holes of generalized Reed-Solomon codes. (English) Zbl 1469.94134

Summary: Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [ Sci. China, Math. 55, No. 12, 2447–2455 (2012; Zbl 1262.94026)], 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.

MSC:

94B05 Linear codes (general theory)
94B25 Combinatorial codes

Citations:

Zbl 1262.94026
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References:

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