The period of $x^h + x + 1$ over GF(2)
<|reference_start|>The period of $x^h + x + 1$ over GF(2): 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.<|reference_end|>
@article{nguyen2024the,
    title={The period of $x^h + x + 1$ over GF(2)},
    author={Gam D. Nguyen},
    journal={arXiv preprint arXiv:2408.14820},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.14820},
    primaryClass={cs.IT math.IT}
}