On deep holes of generalized Reed-Solomon codes
نویسندگان
چکیده
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.
منابع مشابه
New 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 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...
متن کاملA general construction of Reed-Solomon codes based on generalized discrete Fourier transform
In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.
متن کاملOn 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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1205.7016 شماره
صفحات -
تاریخ انتشار 2012