A Construction of Arbitrarily Large Type-II $Z$ Complementary Code Set
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916244588855296 |
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| author | Kumar, Rajen Srivastava, Prashant Kumar Majhi, Sudhan |
| author_facet | Kumar, Rajen Srivastava, Prashant Kumar Majhi, Sudhan |
| contents | For a type-I $(K,M,Z,N)$-ZCCS, it follows $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. In this paper, we propose a construction of type-II $(p^{k+n},p^k,p^{n+r}-p^r+1,p^{n+r})$-$Z$ complementary code set (ZCCS) using an extended Boolean function, its properties of Hamiltonian paths and the concept of isolated vertices, where $p\ge 2$. However, the proposed type-II ZCCS provides $K = M(N-Z+1)$ codes, where as for type-I $(K,M,N,Z)$-ZCCS, it is $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. Therefore, the proposed type-II ZCCS provides a larger number of codes compared to type-I ZCCS. Further, as a special case of the proposed construction, $(p^k,p^k,p^n)$-CCC can be generated, for any integral value of $p\ge2$ and $k\le n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01290 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Construction of Arbitrarily Large Type-II $Z$ Complementary Code Set Kumar, Rajen Srivastava, Prashant Kumar Majhi, Sudhan Information Theory For a type-I $(K,M,Z,N)$-ZCCS, it follows $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. In this paper, we propose a construction of type-II $(p^{k+n},p^k,p^{n+r}-p^r+1,p^{n+r})$-$Z$ complementary code set (ZCCS) using an extended Boolean function, its properties of Hamiltonian paths and the concept of isolated vertices, where $p\ge 2$. However, the proposed type-II ZCCS provides $K = M(N-Z+1)$ codes, where as for type-I $(K,M,N,Z)$-ZCCS, it is $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. Therefore, the proposed type-II ZCCS provides a larger number of codes compared to type-I ZCCS. Further, as a special case of the proposed construction, $(p^k,p^k,p^n)$-CCC can be generated, for any integral value of $p\ge2$ and $k\le n$. |
| title | A Construction of Arbitrarily Large Type-II $Z$ Complementary Code Set |
| topic | Information Theory |
| url | https://arxiv.org/abs/2305.01290 |