A Root-finding algorithm for list decoding of Reed-Muller codes
- Authors: Wu, Xinwen , Kuijper, Margreta , Udaya, Parampalli
- Date: 2006
- Type: Text , Journal article
- Relation: IEEE transactions on information theory Vol. 51, no. 3 (2006), p. 1190-1196
- Full Text: false
- Reviewed:
- Description: Let Fq[X1,...,Xm] denote the set of polynomials over Fq in m variables, and Fq[X1,...,Xm]≤u denote the subset that consists of the polynomials of total degree at most u. Let H(T) be a nontrivial polynomial in T with coefficients in Fq[X1,...,Xm]. A crucial step in interpolation-based list decoding of q-ary Reed-Muller (RM) codes is finding the roots of H(T) in Fq[X1,...,Xm]≤u. In this correspondence, we present an efficient root-finding algorithm, which finds all the roots of H(T) in Fq[X1,...,Xm]≤u. The algorithm can be used to speed up the list decoding of RM codes.
- Description: C1
- Description: 2003005726
Lower bound on minimum lee distance of algebraic-geometric codes over finite fields
- Authors: Wu, Xinwen , Kuijper, Margreta , Udaya, Parampalli
- Date: 2007
- Type: Text , Journal article
- Relation: Electronics Letters Vol. 43, no. 15 (2007), p. 820-822
- Full Text:
- Reviewed:
- Description: Algebraic-geometric (AG) codes over finite fields with respect to the Lee metric have been studied. A lower bound on the minimum Lee distance is derived, which is a Lee-metric version of the well-known Goppa bound on the minimum Hamming distance of AG codes. The bound generalises a lower bound on the minimum Lee distance of Lee-metric BCH and Reed-Solomon codes, which have been successfully used for protecting against bitshift and synchronisation errors in constrained channels and for error control in partial-response channels.
- Description: C1
- Description: 2003005654