Generalized modified Gold sequences

Zhou, Zhengchun; Tang, Xiaohu

doi:10.1007/s10623-010-9430-8

Cited by 9 publications

(4 citation statements)

References 12 publications

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“…It follows from the definition of C (q, m, δ 3 ) and Lemmas 1, 3 and 8 that the check polynomial of this One can refine the proofs in [20], [32], [31] and [33], to prove that d = δ 3 . We omit the lengthy details here.…”

Section: Weight Wmentioning

confidence: 76%

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The dimension and minimum distance of two classes of primitive BCH codes

Ding

Fan

Zhou

2017

Finite Fields and Their Applications

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Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes -a family of cyclic codes -in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the narrow-sense primitive BCH codes. However, the dimension and minimum distance of these codes are not known in general. The objective of this paper is to determine the dimension and minimum distances of two classes of narrow-sense primitive BCH codes with design distances δ = (q − 1)q m−1 − 1 − q ⌊(m−1)/2⌋ and δ = (q − 1)q m−1 − 1 − q ⌊(m+1)/2⌋ . The weight distributions of some of these BCH codes are also reported. As will be seen, the two classes of BCH codes are sometimes optimal and sometimes among the best linear codes known.

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Section: Weight Wmentioning

confidence: 76%

“…Similarly, the weights and their frequencies of the codewords in C (q, m, δ 3 ) are determined by the affine and quadratic functions Tr ax + bx 1+q ⌊(m−1)/2⌋+1 + cx 1+q ⌊(m+1)/2⌋+1 + e. One can refine the proofs in [20], [32], [31] and [33], to prove that d = δ 3 . We omit the lengthy details here.…”

Section: Weight Wmentioning

confidence: 95%

The dimension and minimum distance of two classes of primitive BCH codes

Ding

Fan

Zhou

2017

Finite Fields and Their Applications

Self Cite

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“…Many sequence sets with low correlation have been reported [1][2][3][4][5][6][7][8][9]. However, only a few sequence sets can attain the Welch's bound or Sidelnokiv's bound , for example the Kasami sequences [1], the Gold sequences [2], the Sidelnikov sequences [3], the bent sequences [4], and the Gold-like sequences [6].…”

Section: Introductionmentioning

confidence: 99%

New constructions of low-correlation sequences with high-linear complexity

Xiong¹,

Li²,

Dai³

et al. 2012

IET Commun.

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Abstract. In this paper, we propose a new concept named similar-bent function and we present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. We find that the bent sequence sets are special cases of our construction. We also investigate the linear complexity of the new constructed sequences. If a suitable similar-bent function is given, the sequences constructed by it can have high linear complexity. As examples, we construct two new low correlation sequence sets. One constructed based on Dobbertin's iterative function is asymptotically optimal with respect to Welch's bound and the other one is constructed based on Kasami function whose sequences have a high linear complexity.

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“…Besides, there are some known families of sequences of length 2 n − 1 with good correlation properties, such as bent function sequences [21], No sequences [19], and Trace Norm sequences [13]. In 2011, Zhou and Tang generalized the modified Gold sequences and obtained a family of binary sequences with length 2 n − 1 for n = 2m + 1, size 2 ℓn + • • •+ 2 n − 1, and correlation 2 m+ℓ + 1 for each 1 ℓ m [35]. In addition to the above mentioned sequences of length 2 n − 1, there is some work devoted to the construction of good binary sequences with length of forms such as 2(2 n − 1) and (2 n − 1) 2 [30], [29], [28], [6].…”

Section: Introductionmentioning

confidence: 99%

Binary Sequences With a Low Correlation via Cyclotomic Function Fields

Jin

Xing

2022

IEEE Trans. Inform. Theory

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Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary sequences attracts great attention. As a result, various constructions of good binary sequences have been proposed. However, most of the known constructions made use of the multiplicative cyclic group structure of finite field F p n for a prime p and a positive integer n. In fact, all p n + 1 rational places including the place at infinity of the rational function field over F p n form a cyclic structure under an automorphism of order p n + 1. In this paper, we make use of this cyclic structure to provide an explicit construction of binary sequences with a low correlation of length p n +1 via cyclotomic function fields over F p n for any odd prime p. Each family of binary sequences has size p n − 2 and its correlation is upper bounded by 4 + ⌊2 • p n/2 ⌋. To the best of our knowledge, this is the first construction of binary sequences with a low correlation of length p n + 1 for odd prime p. Moreover, our sequences can be constructed explicitly and have competitive parameters.

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Generalized modified Gold sequences

Cited by 9 publications

References 12 publications

The dimension and minimum distance of two classes of primitive BCH codes

The dimension and minimum distance of two classes of primitive BCH codes

New constructions of low-correlation sequences with high-linear complexity

Binary Sequences With a Low Correlation via Cyclotomic Function Fields

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