Golay Complementary Sequences of Arbitrary Length and Asymptotic Existence of Hadamard Matrices
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911766196256768 |
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| author | Du, Cheng Jiang, Yi |
| author_facet | Du, Cheng Jiang, Yi |
| contents | In this work, we construct $4$-phase Golay complementary sequence (GCS) set of cardinality $2^{3+\lceil \log_2 r \rceil}$ with arbitrary sequence length $n$, where the $10^{13}$-base expansion of $n$ has $r$ nonzero digits. Specifically, the GCS octets (eight sequences) cover all the lengths no greater than $10^{13}$. Besides, based on the representation theory of signed symmetric group, we construct Hadamard matrices from some special GCS to improve their asymptotic existence: there exist Hadamard matrices of order $2^t m$ for any odd number $m$, where $t = 6\lfloor \frac{1}{40}\log_{2}m\rfloor + 10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Golay Complementary Sequences of Arbitrary Length and Asymptotic Existence of Hadamard Matrices Du, Cheng Jiang, Yi Information Theory In this work, we construct $4$-phase Golay complementary sequence (GCS) set of cardinality $2^{3+\lceil \log_2 r \rceil}$ with arbitrary sequence length $n$, where the $10^{13}$-base expansion of $n$ has $r$ nonzero digits. Specifically, the GCS octets (eight sequences) cover all the lengths no greater than $10^{13}$. Besides, based on the representation theory of signed symmetric group, we construct Hadamard matrices from some special GCS to improve their asymptotic existence: there exist Hadamard matrices of order $2^t m$ for any odd number $m$, where $t = 6\lfloor \frac{1}{40}\log_{2}m\rfloor + 10$. |
| title | Golay Complementary Sequences of Arbitrary Length and Asymptotic Existence of Hadamard Matrices |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.15381 |