Construction of Some Good Binary Linear Codes Using Hadamard Matrix and BCH Codes

Khebbou, Driss; Benkhouya, Reda; Chana, Idriss

doi:10.1007/978-981-16-2377-6_49

Cited by 4 publications

(13 citation statements)

References 9 publications

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“…Three types of results are presented in this section; the first one is obtained by the new method mentioned in the previous section, the second is an extension of [7] for the Golay and Reed-Muller codes, and the third one is based on the codes of the first result. All programs have been implemented in GAP via the GUAVA package over 𝔽 2 and 𝔽 3 [18].…”

Section: Resultsmentioning

confidence: 99%

“…it allows to design many good binary linear block codes with considerable errorcorrecting capability. This method extends the approach presented in [7] for larger dimensions by exploiting the MacWilliams identity to overcome the problem of computing the minimal distance on the one hand, and to confirm the technique for codes other than BCH codes [8] on the other hand.…”

Section: Introductionmentioning

confidence: 85%

“…In [7], a method based on the outcome of the Kronecker product, between the Hadamard matrix and the redundant part of a generator matrix of a Bose, Ray-Chaudhuri et Hocquenghem (BCH) code is presented, to construct good binary linear codes. It allows us, from a (𝑙𝑙, 𝑒𝑒, 𝑑𝑑 𝑚𝑖𝑛 ) BCH code and a Hadamard matrix of order 𝑚𝑚, to build good binary linear codes having a given dimension 𝑒𝑒' < 20 and length 𝑙𝑙′ = 𝑚𝑚 * 𝑙𝑙.…”

Section: New Methods To Find Good Binary Linear Codesmentioning

confidence: 99%

“…So for dimensions 𝑒𝑒' > 20, the method presented in [7] remains restricted according to the performance of a simple computer to calculate the minimum distance for codes with dimensions greater than 20. In this work, we practically took advantage of the dual properties of linear block codes and MacWilliams identity as it can be seen in figure 1 and outlined in the steps bellow, in order to fix this issue and validate the process by constructing good codes with high dimensions.…”

Section: New Methods To Find Good Binary Linear Codesmentioning

confidence: 99%

“…One of the most recent methods to construct good binary linear block codes is presented in [7]. It consists in constructing linear codes from the Hadamard matrix and Bose-Chaudhuri-Hocquenghem (BCH) codes [8].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Finding Good Binary Linear Block Codes based on Hadamard Matrix and Existing Popular Codes

Khebbou¹,

Benkhouya²,

Chana³

et al. 2021

IJACSA

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Because of their algebraic structure and simple hardware implementation, linear codes as class of errorcorrecting codes, are used in a multitude of situations such as Compact disk, backland bar code, satellite and wireless communication, storage systems, ISBN numbers and so more. Nevertheless, the design of linear codes with high minimum Hamming distance to a given dimension and length of the code, remains an open challenge in coding theory. In this work, we propose a code construction method for constructing good binary linear codes from popular ones, while using the Hadamard matrix. The proposed method takes advantage of the MacWilliams identity for computing the weight distribution, to overcome the problem of computing the minimum Hamming distance for larger dimensions.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 85%

Section: New Methods To Find Good Binary Linear Codesmentioning

confidence: 99%

Section: New Methods To Find Good Binary Linear Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finding Good Binary Linear Block Codes based on Hadamard Matrix and Existing Popular Codes

Khebbou¹,

Benkhouya²,

Chana³

et al. 2021

IJACSA

Self Cite

View full text Add to dashboard Cite

show abstract

Single parity check node adapted to polar codes with dynamic frozen bit equivalent to binary linear block codes

Khebbou

Chana²,

Ben-Azza³

2023

IJEECS

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<span lang="EN-US">In the context of decoding binary linear block codes by polar code decoding techniques, we propose in this paper a new optimization of the serial nature of decoding the polar codes equivalent to binary linear block codes. In addition to the special nodes proposed by the simplified successive-cancellation list technique, we propose a new special node allowing to estimate in parallel the bits of its sub-code. The simulation is done in an additive white gaussian noise channel (AWGN) channel for several linear block codes, namely bose–chaudhuri–hocquenghem codes (BCH) codes, quadratic-residue (QR) codes, and linear block codes recently designed in the literature. The performance of the proposed technique offers the same performance in terms of frame error rate (FER) as the ordered statistics decoding (OSD) algorithm, which achieves that of maximum likelihood decoder (MLD), but with high memory requirements and computational complexity.</span>

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Decoding of the extended Golay code by the simplified successive-cancellation list decoder adapted to multi-kernel polar codes

2023

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This paper describes an adaptation of a polar code decoding technique in favor of the extended Golay code. Based on the bridge provided by a permutation matrix between the code words of these two classes of codes, the Golay code can be decoded by any polar code technique. Contrary to the successive-cancellation list technique which is characterized by a serial estimation of the bits, we propose in this work an adaptation of the simplified successive-cancellation list technique to polar codes equivalent to the Golay code. The simulations have achieved the performance of a maximum likelihood decoding, with the low decoding complexity of polar codes, compared to one of the universal decoders of linear codes most known in the literature.

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Construction of Some Good Binary Linear Codes Using Hadamard Matrix and BCH Codes

Cited by 4 publications

References 9 publications

Finding Good Binary Linear Block Codes based on Hadamard Matrix and Existing Popular Codes

Finding Good Binary Linear Block Codes based on Hadamard Matrix and Existing Popular Codes

Single parity check node adapted to polar codes with dynamic frozen bit equivalent to binary linear block codes

Decoding of the extended Golay code by the simplified successive-cancellation list decoder adapted to multi-kernel polar codes

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