Decoding Linear Codes
نویسنده
چکیده
We mention four recent results, none of which has appeared yet. They come from different sources. The purpose of these notes is to present them in a short way. Two results concern the generalization of the Roos-bound from cyclic codes to more general linear codes. Two others concern the use of majority coset decoding to the decoding of cyclic codes. ∗Supported by NWO, The Netherlands. Prepared for a visit to INRIA, Paris, March 18-22. Current address: LMD Equipe ATI, Case 930, 13288 MARSEILLE CEDEX 9. E-mail: [email protected].
منابع مشابه
Linear codes with complementary duals related to the complement of the Higman-Sims graph
In this paper we study codes $C_p(overline{{rm HiS}})$ where $p =3,7, 11$ defined by the 3- 7- and 11-modular representations of the simple sporadic group ${rm HS}$ of Higman and Sims of degree 100. With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes ha...
متن کاملDuality for Modules and Applications to Decoding Linear Codes over Finite Commutative Rings
Syndrome decoding is a more efficient method of decoding linear codes over finite fields over a noisy channel [5]. Thus, in this paper we investigate the generalization of the syndrome decoding to linear codes over finite commutative rings. A first generalization was given in [1] via Pontryagin duality. In the same direction we give another generalization using linear functional-based duality. ...
متن کاملSearch Based Weighted Multi-Bit Flipping Algorithm for High-Performance Low-Complexity Decoding of LDPC Codes
In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...
متن کاملExtending LP-Decoding for Permutation Codes from Euclidean to Kendall tau Metric
Invented in the 1960’s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications. In 2011 a decoding method called LP (linear programming) decoding was introduced for a class of permutation codes with a Euclidean distance induced metric. In this paper we comparatively analyze the Eucl...
متن کاملLinear Block Codes: Encoding and Syndrome Decoding
The previous chapter defined some properties of linear block codes and discussed two examples of linear block codes (rectangular parity and the Hamming code), but the approaches presented for decoding them were specific to those codes. Here, we will describe a general strategy for encoding and decoding linear block codes. The decoding procedure we describe is syndrome decoding, which uses the s...
متن کاملPermutation decoding of Z 2 Z 4 - linear codes
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear codes, which are binary and, in general, nonlinear codes in the usual sense. For this, it is proved that these codes allow a systematic encoding scheme. As pa...
متن کامل