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 whichwe 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 pk, 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.

Automated summary

This paper proposes a direct construction method for a novel code set called complete complementary-ZCZ (CC-ZCZ) code set, which combines the properties of complete complementary code (CCC) and zero correlation zone (ZCZ) sequence set. The construction method involves the use of multivariate functions and also provides Golay-ZCZ codes of prime-power lengths. The optimal and asymptotically optimal properties of the proposed Golay-ZCZ codes are proven for binary and non-binary cases respectively by the Tang-Fan-Matsufuzi bound. Additionally, the proposed construction method yields novel ZCZ sequences of length pk, where p is a prime number and k is an integer >= 2. The paper establishes a relationship between the proposed CC-ZCZ code set and the first-order generalized Reed-Muller (GRM) code, showing that both have the same Hamming distance. Furthermore, the column sequence peak-to-mean envelope power ratio (PMEPR) of the CC-ZCZ code set is derived and compared with existing works, along with the derivation and comparison of Golay-ZCZ codes and ZCZ sequences. The proposed construction method generalizes many existing works.