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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2408.14820 |
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| _version_ | 1866916370927583232 |
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| author | Nguyen, Gam D. |
| author_facet | Nguyen, Gam D. |
| contents | The periods of polynomials can be used to characterize discrete structures such as algebraic error control codes and feedback shift registers. We study trinomial $x^h+x+1$ over GF(2), which has the maximum number of consecutive zero coefficients and leads to efficient implementation. Existing results typically deal with finite values of $h$ and rely on computer computation methods for finding the periods. In contrast, here we derive closed-form expressions for the periods of this trinomial for infinite sets of $h$ values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The period of $x^h + x + 1$ over GF(2) Nguyen, Gam D. Information Theory The periods of polynomials can be used to characterize discrete structures such as algebraic error control codes and feedback shift registers. We study trinomial $x^h+x+1$ over GF(2), which has the maximum number of consecutive zero coefficients and leads to efficient implementation. Existing results typically deal with finite values of $h$ and rely on computer computation methods for finding the periods. In contrast, here we derive closed-form expressions for the periods of this trinomial for infinite sets of $h$ values. |
| title | The period of $x^h + x + 1$ over GF(2) |
| topic | Information Theory |
| url | https://arxiv.org/abs/2408.14820 |