Algebraic Decoding of a Class of Binary Cyclic Codes Via Lagrange Interpolation Formula

Chang, Yaotsu; Lee, Chong-Dao

doi:10.1109/tit.2009.2034799

Cited by 21 publications

(44 citation statements)

References 15 publications

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“…Finally, the proposed unified unknown syndrome representation algorithm implemented on an INTEL Core i3 530 personal computer has been verified through a software simulation using C++ language. For the (17,9,5), (23,12,7) and (41, 21,9) quadratic residue codes, experimental results show that the method presented here is faster than the Lagrange interpolation method developed previously in [12]. An illustrative example of decoding the (31, 16,7) quadratic residue code by the inverse-free BerlekampMassey algorithm is also shown.…”

Section: Introductionmentioning

confidence: 90%

“…1. To solve this problem, Chang et al [19] proposed a multivariate interpolation formula over finite fields, which is a generalised result of Chang and Lee [12].…”

Section: Polynomial In Terms Of Syndromesmentioning

confidence: 99%

“…Proof: It is sufficient to verify that the rational function defined by (14) satisfies (12). Without loss of generality, assume that only one error occurred, that is, v ¼ 1.…”

Section: Modified Chinese Remainder Theoremmentioning

confidence: 99%

“…Two non-iterative decoding schemes of binary cyclic codes have been recently developed based on the general error locator polynomials [10,11] and unified unknown syndrome representations [12], respectively. Since then, variations of general error locator polynomials have been studied in a series of papers [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…This paper, on the contrary, is devoted to the study of the unified unknown syndrome representations. Although the Lagrange interpolation formula [12] is a practical approach to determine the unified unknown syndrome representations, its computational time grows substantially as the number of errors increases. For this reason, it is desirable to have a computationally efficient method before the online decoding, which can be employed without waiting for a long time to the determinations of unified unknown syndrome representations.…”

Section: Introductionmentioning

confidence: 99%

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New method of predetermining unified unknown syndrome representations for decoding binary cyclic codes

et al. 2012

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Recently, the unified unknown syndrome representations to decode a class of binary cyclic codes have been developed by using Lagrange interpolation formula (discussed by Chang and Lee in 2010). In this study, a new method by combining the syndrome matrix search and modified Chinese remainder theorem is proposed to express the unified unknown syndrome representation as a rational function in terms of the known syndromes. A computer simulation has been executed to determine the syndrome matrices for binary cyclic codes of lengths less than or equal to 51. Compared to the Lagrange interpolation method, the method presented here substantially reduces the computational time for binary cyclic codes generated by irreducible polynomials. Finally, a complete decoding of the (31, 16, 7) quadratic residue code with inverse-free Berlekamp-Massey algorithm is given as an illustration.

show abstract

Section: Introductionmentioning

confidence: 90%

“…1. To solve this problem, Chang et al [19] proposed a multivariate interpolation formula over finite fields, which is a generalised result of Chang and Lee [12].…”

Section: Polynomial In Terms Of Syndromesmentioning

confidence: 99%

“…Proof: It is sufficient to verify that the rational function defined by (14) satisfies (12). Without loss of generality, assume that only one error occurred, that is, v ¼ 1.…”

Section: Modified Chinese Remainder Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New method of predetermining unified unknown syndrome representations for decoding binary cyclic codes

et al. 2012

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Improved decoding of affine-variety codes

Marcolla

Orsini

Sala

2012

Journal of Pure and Applied Algebra

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General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding techniques for affine-variety codes using some multidimensional extensions of general error locator polynomials. We prove the existence of such polynomials for any correctable affine-variety code and hence for any linear code. We propose two main different approaches, that depend on the underlying geometry. We compute some interesting cases, including Hermitian codes. To prove our coding theory results, we develop a theory for special classes of zero-dimensional ideals, that can be considered generalizations of stratified ideals. Our improvement with respect to stratified ideals is twofold: we generalize from one variable to many variables and we introduce points with multiplicities

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Fast algebraic decoding of the (17, 9, 5) quadratic residue code

Lee

2012

2012 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet)

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Algebraic Decoding of a Class of Binary Cyclic Codes Via Lagrange Interpolation Formula

Cited by 21 publications

References 15 publications

New method of predetermining unified unknown syndrome representations for decoding binary cyclic codes

New method of predetermining unified unknown syndrome representations for decoding binary cyclic codes

Improved decoding of affine-variety codes

Fast algebraic decoding of the (17, 9, 5) quadratic residue code

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