Some new results on dimension and Bose distance for various classes of BCH codes

Cherchem, Ahmed; Jamous, Abdelillah; Liu, Hongwei; Maouche, Youcef

doi:10.1016/j.ffa.2020.101673

Cited by 13 publications

(14 citation statements)

References 10 publications

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“…3. We present the dimension and the Bose distance of three families of the narrow-sense primitive BCH codes with designed distances δ (a,c) = 4 Based on the results in [6], we generalize some results of the code C (n,q,δ) , where…”

Section: Introductionmentioning

confidence: 85%

“…We present a corollary, which holds from Proposition 2.2 and can be found in [6]. It will be often used in the sequel.…”

Section: Proposition 22 the Bose Distance D B Of The Codementioning

confidence: 93%

“…Now we determine the dimension and the Bose distance of the code C (n,q,δ (a,c) ) . The case c = 0 has been studied in [6], so we focus on c ≥ 1.…”

Section: The Dimension and The Bose Distance Of The Narrow-sense Primitive Bch Codesmentioning

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%

“…Finally, we give the conclusion of the paper in Sect. 6 In this paper, we compare the BCH codes obtained with the tables of the best linear codes known maintained by Markus Grassl at http://www.codetables.de, which is called the Database subsequently.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 85%

“…We present a corollary, which holds from Proposition 2.2 and can be found in [6]. It will be often used in the sequel.…”

Section: Proposition 22 the Bose Distance D B Of The Codementioning

confidence: 93%

“…Now we determine the dimension and the Bose distance of the code C (n,q,δ (a,c) ) . The case c = 0 has been studied in [6], so we focus on c ≥ 1.…”

Section: The Dimension and The Bose Distance Of The Narrow-sense Primitive Bch Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Pang

Zhu

Kai

2021

Des. Codes Cryptogr.

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A class of narrow-sense BCH codes over $$\mathbb {F}_q$$ of length $$\frac{q^m-1}{2}$$

Ling

Mesnager

et al. 2019

Des. Codes Cryptogr.

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BCH codes are an important class of cyclic codes, and have wide applications in communication and storage systems. In this paper, we study the negacyclic BCH code and cyclic BCH code of lengthThe dimensions of negacyclic BCH codes C (n,−1,δ,0) with few nonzeros and C (n,−1,δ,b) with b = 1 are settled. For cyclic BCH code, we give the weight distributions of extended codes C (n,1,δ,1) for δ = δ 1 , δ 2 and the parameters of dual code C ⊥ (n,1,δ,1) for δ 2 ≤ δ ≤ δ 1 .

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