A Direct Construction of Complete Complementary Code with Zero Correlation Zone Property for Prime-Power Length
Cryptography and communications(2023)
Abstract
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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Key words
Golay complementary sets (GCSs),Complete complementary code (CCC),Multivariate functions,Zero correlation zone (ZCZ) sequence set,Golay-ZCZ sequence set,Complete complementary-zero correlation zone (CC-ZCZ) code set,Prime-power length,Peak-to-mean envelope power ratio (PMEPR),Orthogonal frequency division multiplexing (OFDM),Multi-carrier code division multiple access (MC-CDMA),Generalized Reed-Muller (GRM) codes,94A05,94A15,94A55,94B60
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