On deep holes of primitive projective 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...
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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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Reed-Solomon codes were formally introduced to the world in 1960, and have been both practically and theoretically interesting since their introducion. Used in CD players, long-distance space communication, and computer networks, these simple codes have fascinated coding theorists and theoretical computer scientists for nearly five decades. In addition to being one of the Maximum Distance Seper...
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For generalized Reed-Solomon codes, it has been proved [6] that the problem of determining if a received word is a deep hole is co-NP-complete. The reduction relies on the fact that the evaluation set of the code can be exponential in the length of the code – a property that practical codes do not usually possess. In this paper, we first presented a much simpler proof of the same result. We the...
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Determining deep holes is an important open problem in decoding ReedSolomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the ReedSolomon code. For the standard Reed-Solomon codes [p − 1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the tr...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2018
ISSN: 1674-7216
DOI: 10.1360/n012017-00064