A direct construction of complete complementary code with zero correlation zone property for prime-power length

In this paper, we propose a direct construction of a novel type of code set which has combined properties of complete complementary code (CCC) and zero correlation zone (ZCZ) sequence set and which we call complete complementary-ZCZ (CC-ZCZ) code set. The code set is constructed using multivariate f...

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Bibliographic Details
Published in:Cryptography and communications Vol. 16; no. 2; pp. 403 - 426
Main Authors: Kumar, Nishant, Majhi, Sudhan, Upadhyay, Ashish K.
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2024
Springer Nature B.V
Subjects:
Circuits
Code Division Multiple Access
Coding and Information Theory
Communications Engineering
Computer Science
Construction
Data Structures and Information Theory
Information and Communication
Mathematics of Computing
Networks
Prime numbers
Sequences
Zero correlation zone (ZCZ) sequence set
Golay complementary sets (GCSs)
Peak-to-mean envelope power ratio (PMEPR)
Complete complementary code (CCC)
Multi-carrier code division multiple access (MC-CDMA)
Golay-ZCZ sequence set
Prime-power length
Multivariate functions
Orthogonal frequency division multiplexing (OFDM)
94A05
94A15
Generalized Reed-Muller (GRM) codes
94B60
Complete complementary-zero correlation zone (CC-ZCZ) code set
94A55
ISSN:1936-2447, 1936-2455
Online Access:Get full text
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Summary:In this paper, we propose a direct construction of a novel type of code set which has combined properties of complete complementary code (CCC) and zero correlation zone (ZCZ) sequence set and which we call complete complementary-ZCZ (CC-ZCZ) code set. The code set is constructed using multivariate functions. The proposed construction also provides Golay-ZCZ codes of prime-power lengths. The proposed Golay-ZCZ codes are optimal and asymptotically optimal for binary and non-binary cases, respectively, by Tang-Fan-Matsufuzi bound. Furthermore, the proposed direct construction provides novel ZCZ sequences of length p k , where p is a prime number and k is an integer ≥ 2 . We establish a relationship between the proposed CC-ZCZ code set and the first-order generalized Reed-Muller (GRM) code, and prove that both have the same Hamming distance. We also count the number of CC-ZCZ code sets in first-order GRM codes. The column sequence peak-to-mean envelope power ratio (PMEPR) of the proposed CC-ZCZ code set is derived and compared with existing works. From the proposed construction, the Golay-ZCZ code and ZCZ sequences are also derived and compared with the existing works. The proposed construction generalizes many of the existing works.
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ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-023-00676-w