Construction of CCC and ZCCS Through Additive Characters Over Galois Field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913497502187520 |
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| author | Ghosh, Gobinda Pathak, Sachin |
| author_facet | Ghosh, Gobinda Pathak, Sachin |
| contents | The rapid progression in wireless communication technologies, especially in multicarrier code-division multiple access (MC-CDMA), there is a need of advanced code construction methods. Traditional approaches, mainly based on generalized Boolean functions, have limitations in code length versatility. This paper introduces a novel approach to constructing complete complementary codes (CCC) and Z-complementary code sets (ZCCS), for reducing interference in MC-CDMA systems. The proposed construction, distinct from Boolean function-based approaches, employs additive characters over Galois fields GF($p^{r}$), where $p$ is prime and $r$ is a positive integer. First, we develop CCCs with lengths of $p^{r}$, which are then extended to construct ZCCS with both unreported lengths and sizes of $np^{r}$, where $n$ are arbitrary positive integers. The versatility of this method is further highlighted as it includes the lengths of ZCCS reported in prior studies as special cases, underscoring the method's comprehensive nature and superiority. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of CCC and ZCCS Through Additive Characters Over Galois Field Ghosh, Gobinda Pathak, Sachin Information Theory Combinatorics The rapid progression in wireless communication technologies, especially in multicarrier code-division multiple access (MC-CDMA), there is a need of advanced code construction methods. Traditional approaches, mainly based on generalized Boolean functions, have limitations in code length versatility. This paper introduces a novel approach to constructing complete complementary codes (CCC) and Z-complementary code sets (ZCCS), for reducing interference in MC-CDMA systems. The proposed construction, distinct from Boolean function-based approaches, employs additive characters over Galois fields GF($p^{r}$), where $p$ is prime and $r$ is a positive integer. First, we develop CCCs with lengths of $p^{r}$, which are then extended to construct ZCCS with both unreported lengths and sizes of $np^{r}$, where $n$ are arbitrary positive integers. The versatility of this method is further highlighted as it includes the lengths of ZCCS reported in prior studies as special cases, underscoring the method's comprehensive nature and superiority. |
| title | Construction of CCC and ZCCS Through Additive Characters Over Galois Field |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2402.09757 |