New Constructions of Asymptotically Optimal Codebooks via Cyclotomic Classes of Order 8

Asymptotically optimal codebooks are a family of codebooks that can approach an optimal codebook meeting the Welch bound when the lengths of codewords are large enough. They can be constructed easily and are a good alternative for optimal codebooks in many applications. In this paper, we construct a new class of asymptotically optimal codebooks by using the product of some special finite fields and almost difference sets, which are composed of cyclotomic classes of order eight.

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Some new almost difference sets via finite fields

ACM Communications in Computer Algebra ◽

10.1145/2768577.2768608 ◽

2015 ◽

Vol 49 (1) ◽

pp. 21-22

Author(s):

Bo Phillips ◽

Jace Robinson

Keyword(s):

Finite Fields ◽

Difference Sets ◽

Almost Difference Sets

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Constructions of almost difference sets from finite fields

Designs Codes and Cryptography ◽

10.1007/s10623-012-9789-9 ◽

2013 ◽

Vol 72 (3) ◽

pp. 581-592 ◽

Cited By ~ 10

Author(s):

Cunsheng Ding ◽

Alexander Pott ◽

Qi Wang

Keyword(s):

Finite Fields ◽

Difference Sets ◽

Almost Difference Sets

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Linear Array Thinning Exploiting Almost Difference Sets

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2009.2027243 ◽

2009 ◽

Vol 57 (12) ◽

pp. 3800-3812 ◽

Cited By ~ 114

Author(s):

G. Oliveri ◽

M. Donelli ◽

A. Massa

Keyword(s):

Linear Array ◽

Difference Sets ◽

Almost Difference Sets

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A new class of quaternary generalized cyclotomic sequences of order 2d and length 2pm with high linear complexity

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691318500066 ◽

2018 ◽

Vol 16 (01) ◽

pp. 1850006 ◽

Cited By ~ 3

Author(s):

Longfei Liu ◽

Xiaoyuan Yang ◽

Bin Wei ◽

Liqiang Wu

Keyword(s):

Finite Fields ◽

Linear Complexity ◽

Periodic Sequences ◽

New Class ◽

New Family ◽

Generalized Cyclotomic Classes ◽

Cyclotomic Sequences

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order [Formula: see text] and length [Formula: see text], which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.

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More Quasi-Complementary Sequence Sets from Difference Sets and Almost Difference Sets

2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA) ◽

10.1109/iwsda46143.2019.8966099 ◽

2019 ◽

Author(s):

Yubo Li ◽

Chengqian Xu ◽

Xiuping Peng

Keyword(s):

Difference Sets ◽

Complementary Sequence ◽

Almost Difference Sets

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On Some New Families of Almost Difference Sets Constructed From Cyclotomic Classes of Order 12

IEEE Communications Letters ◽

10.1109/lcomm.2015.2503279 ◽

2016 ◽

Vol 20 (1) ◽

pp. 61-64

Author(s):

Minglong Qi ◽

Shengwu Xiong ◽

Jingling Yuan ◽

Wenbi Rao ◽

Luo Zhong

Keyword(s):

Difference Sets ◽

Almost Difference Sets

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Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound

Advances in Mathematics of Communications ◽

10.3934/amc.2021065 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Gang Wang ◽

Deng-Ming Xu ◽

Fang-Wei Fu

Keyword(s):

Code Division Multiple Access ◽

Communication Systems ◽

Multiple Access ◽

Cross Correlation ◽

Hadamard Matrices ◽

Circulant Matrices ◽

Asymptotically Optimal ◽

Welch Bound ◽

Construction Methods ◽

Code Division Multiple

<p style='text-indent:20px;'>Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.</p>

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