Deep holes of generalized Reed-Solomon codes
نویسندگان
چکیده
منابع مشابه
On deep holes of generalized projective Reed-Solomon codes
Abstract. Determining deep holes is an important topic in decoding Reed-Solomon codes. Cheng and Murray, Li and Wan, Wu and Hong investigated the error distance of generalized Reed-Solomon codes. Recently, Zhang and Wan explored the deep holes of projective Reed-Solomon codes. Let l ≥ 1 be an integer and a1, . . . , al be arbitrarily given l distinct elements of the finite field Fq of q element...
متن کاملNew Deep Holes of Generalized Reed-Solomon Codes
Deep holes play an important role in the decoding of generalized Reed-Solomon codes. Recently, Wu and Hong [11] found a new class of deep holes for standard Reed-Solomon codes. In the present paper, we give a concise method to obtain a new class of deep holes for generalized Reed-Solomon codes. In particular, for standard Reed-Solomon codes, we get the new class of deep holes given in [11]. Li ...
متن کاملOn deep holes of generalized Reed-Solomon codes
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...
متن کاملOn Determining Deep Holes of Generalized Reed-Solomon Codes
For a linear code, deep holes are defined to be vectors that are further away from codewords than all other vectors. The problem of deciding whether a received word is a deep hole for generalized ReedSolomon codes is proved to be co-NP-complete [9][5]. For the extended Reed-Solomon codes RSq(Fq, k), a conjecture was made to classify deep holes in [5]. Since then a lot of effort has been made to...
متن کاملExplicit Deep Holes of Reed-Solomon Codes
In this paper, deep holes of Reed-Solomon (RS) codes are studied. A new class of deep holes for generalized affine RS codes is given if the evaluation set satisfies certain combinatorial structure. Three classes of deep holes for projective Reed-Solomon (PRS) codes are constructed explicitly. In particular, deep holes of PRS codes with redundancy three are completely obtained when the character...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2013
ISSN: 1674-7216
DOI: 10.1360/012012-30