On Two Classes of Primitive BCH Codes and Some Related Codes

Li, Chengju; Wu, Peng; Liu, Fengmei

doi:10.1109/tit.2018.2883615

Cited by 31 publications

(12 citation statements)

References 19 publications

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“…As a subclass of BCH codes, Reed-Solomon codes have been widely used in communication devices and consumer electronics. In the past ten years, a lot of progress on the study of BCH codes has been made (see, for example, [16], [17], [18], [19], [25]). In this paper, we will investigate an important application of BCH codes in combinatorial designs.…”

Section: A Cyclic Codes and Bch Codesmentioning

confidence: 99%

An Infinite Family of Linear Codes Supporting 4-Designs

Tang

Ding

2021

IEEE Trans. Inform. Theory

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Section: A Cyclic Codes and Bch Codesmentioning

confidence: 99%

An Infinite Family of Linear Codes Supporting 4-Designs

Tang

Ding

2021

IEEE Trans. Inform. Theory

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“…The BCH codes, discovered in 1960 [13]- [15], is a class of cyclic codes that has well-known implementation algorithms and powerful error-correcting properties [16]. BCH encoder is based on linear feedback shift register (LFSR) as shown in Figure 1 [17].…”

Section: Bch and Convolution Coding Systems 21 Bch Codesmentioning

confidence: 99%

Improving bit error-rate based on adaptive Bose-Chaudhuri Hocquenghem concatenated with convolutional codes

Abdelshafy.

Hassan²,

Zakaria³

2021

IJEECS

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Several algorithms have been proposed to avoid the error floor region, such as the concatenation codes that requires high computational demands in addition to high complexity. This paper proposes a technique based on using cascaded BCH and convolutional codes that leads to better error correction performance. Moreover, an adaptive method based on sensing the channel's noise to determine the number of the parity bits that will be added to the used BCH that reduces the consumed bandwidth and the transmitted parity bits is presented. A further enhancement is fulfilled by using parallel processing branches, resulting in reducing the consumed time and speed up the performance. The results show that the proposed code presents a better performance. A high reduction in the number of cycles that will be used in the encoding and decoding compared with the classical method and finally a flexible parity bits method based on the signal-to-noise ratio of the channel that reduced the parity bits which leads to reduce the consumed bandwidth. The MATLAB simulation and the field programmable gate array (FPGA) implementation will be provided in this paper to validate the proposed concept.

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“…The minimum distance of the code C (n,q, δ) follows from Lemma 3.7. (15,2,5) has parameters [15,7,5]. This code is optimal according to the Database.…”

Section: Lemma 37mentioning

confidence: 99%

“…There are some papers on the narrow-sense primitive BCH codes [1,2,4,9,12,13,17,18,20]. Recently, some excellent survey on parameters of the narrow-sense primitive BCH codes has been given in [6][7][8][9]13,15,19,21]. Next, we list the main known results on the dimension, the Bose distance and the minimum distance of the narrow-sense primitive BCH codes in Table 1.…”

Section: Introductionmentioning

confidence: 99%

Five families of the narrow-sense primitive BCH codes over finite fields

Pang

Zhu

Kai

2021

Des. Codes Cryptogr.

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It is an interesting problem to determine the parameters of BCH codes, due to their wide applications. In this paper, we determine the dimension and the Bose distance of five families of the narrow-sense primitive BCH codes with the following designed distances:Moreover, we obtain the exact parameters of two subfamilies of BCH codes with designed distances δ = b q m −1 q 2 −1 and δ (a,t) = (at+1) q m −1 t(q−1) with even m, 1 ≤ a ≤ q−2 t , 1 ≤ b ≤ q−1, t > 1 and t|(q + 1). Note that we get the narrow-sense primitive BCH codes with flexible designed distance as to a, b, c, t. Finally, we obtain a lot of the optimal or the best narrowsense primitive BCH codes.

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On Two Classes of Primitive BCH Codes and Some Related Codes

Cited by 31 publications

References 19 publications

An Infinite Family of Linear Codes Supporting 4-Designs

An Infinite Family of Linear Codes Supporting 4-Designs

Improving bit error-rate based on adaptive Bose-Chaudhuri Hocquenghem concatenated with convolutional codes

Five families of the narrow-sense primitive BCH codes over finite fields

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