Constacyclic codes over finite fields

Chen, Bocong; Fan, Yun; Lin, Lan; Liu, Hongwei

doi:10.1016/j.ffa.2012.10.001

Cited by 86 publications

(55 citation statements)

References 14 publications

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“…[19,Theorem 3.2] For any λ, µ ∈ F * q , the following three statements are equivalent to each other:…”

mentioning

confidence: 99%

Recent progress on weight distributions of cyclic codes over finite fields

Dinh¹,

Li²,

Yue³

2015

JACODESMATH

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Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions.

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“…[19,Theorem 3.2] For any λ, µ ∈ F * q , the following three statements are equivalent to each other:…”

mentioning

confidence: 99%

Recent progress on weight distributions of cyclic codes over finite fields

Dinh¹,

Li²,

Yue³

2015

JACODESMATH

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“…It is clear that the C 1 is a [5,1] cyclic code and C ⊥ 1 is a [5,4] cyclic code. And A(z) = 1 + (q − 1)z 5 .…”

Section: Lemma 23 ([24]mentioning

confidence: 99%

“…Dinh determined the generator polynomials of all constacyclic codes and their dual codes of length 2p s , 3p s and 6p s over F q in [12,13,14]. Chen et al studied repeated-root constacyclic codes of length l t p s over F q in [5]. In 2014, Chen et al studied all constacyclic codes of length lp s over F q in [3], where l is a prime different from p. In 2015, Raka considered repeated-root constacyclic codes of length l t p s over F q in [20].…”

Section: Introductionmentioning

confidence: 99%

The Hamming distances of repeated-root cyclic codes of length 5ps

Yue

2020

Discrete Applied Mathematics

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Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let p be a prime with p ≥ 7. We determine the weight distributions of all cyclic codes of length 5 over F q and the Hamming distances of all repeated-root cyclic codes of length 5p s over F q , where q = p m and both s and m are positive integers. Furthermore, we find all MDS cyclic codes of length 5p s and take quantum synchronizable codes from repeated-root cyclic codes of length 5p s .

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“…Some families of good quantum codes have been constructed in [4,9,24,26,27,40,45]. Nowadays, some scholars studied some families of constacyclic codes in [5][6][7][8]10,20,25,39]. As we know, constacyclic codes contain cyclic codes and negacyclic codes.…”

Section: Introductionmentioning

confidence: 99%

Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes

Chen

Huang

et al. 2015

Linear Algebra and its Applications

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Quantum maximal-distance-separable (MDS) codes are an important class of quantum codes. Recently, many scholars utilize constacyclic codes to construct some quantum MDS codes. In this paper, several new families of optimal asymmetric quantum codes and optimal quantum convolutional codes are constructed by using constacyclic codes. Moreover, these quantum codes constructed in this paper are different from the ones in the literature.

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Constacyclic codes over finite fields

Abstract: An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length ℓ t p s are characterized, where p is the characteristic of the finite field and ℓ is a prime different from p.

Cited by 86 publications

References 14 publications

Recent progress on weight distributions of cyclic codes over finite fields

Recent progress on weight distributions of cyclic codes over finite fields

The Hamming distances of repeated-root cyclic codes of length 5ps

Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes

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