Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Xiang-Dong Hou"'
Publikováno v:
Finite Fields and Their Applications. 89:102193
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::44a0ba0b36a54352072b9ffb4c3d7a49
https://doi.org/10.1016/j.ffa.2023.102193
https://doi.org/10.1016/j.ffa.2023.102193
Autor:
Xiang-dong Hou
Publikováno v:
IEEE Transactions on Information Theory. 67:5592-5601
Let ${R}_{q}({r},{n})$ be the ${r}$ th order ${q}$ -ary Reed-Muller code of length ${q}^{n}$ , which is the set of functions from ${\mathbb {F}}_{q}^{n}$ to ${\mathbb {F}}_{q}$ represented by polynomials of degree $\le {r}$ in ${\mathbb {F}}_{q}[{X}_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9813f22388f02d17bc00235a939ec0c8
https://doi.org/10.1109/tit.2021.3087157
https://doi.org/10.1109/tit.2021.3087157
Publikováno v:
Finite Fields and Their Applications. 88:102179
After a brief review of existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5db55c16a3842acec65f3fc20a008357
https://doi.org/10.1016/j.ffa.2023.102179
https://doi.org/10.1016/j.ffa.2023.102179
Autor:
Steven T. Dougherty, Gretchen L Matthews, Jay A. Wood, Janet Beissinger, R. Brualdi, Nick Crews, Shmuel Friedland, Xiang-Dong Hou, W Cary Huffman, Jon-Lark Kim, Naomi Pless, Ben Pless, Dan Pless, Patrick Solé, Sarah Spence Adams, Vladimir D. Tonchev, Harold (Thann) Ward, Judy Walker
Publikováno v:
Notices of the American Mathematical Society. 69:1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eac17c49f8b3346de1fba51fba57f2b1
https://doi.org/10.1090/noti2584
https://doi.org/10.1090/noti2584
Autor:
Xiang-dong Hou
Publikováno v:
Communications in Algebra. 48:1640-1649
Let Fq(x) be the field of rational functions over Fq and treat PGL(2,Fq) as the group of degree one rational functions in Fq(x) equipped with composition. PGL(2,Fq) acts on Fq(x) from the r...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16e52ad1948932b5be3bde467ff96b55
https://doi.org/10.1080/00927872.2019.1691582
https://doi.org/10.1080/00927872.2019.1691582
Autor:
Dougherty, Steven T., Matthews, Gretchen L., Wood, Jay A., Beissinger, Janet, Brualdi, Richard, Crews, Nick, Friedland, Shmuel, Xiang-dong Hou, Huffman, W. Cary, Kim, Jon-Lark, Pless, Ben, Pless, Dan, Pless, Naomi, Solé, Patrick, Adams, Sarah Spence, Tonchev, Vladimir D., Walker, Judy, Ward, Harold (Thann)
Publikováno v:
Notices of the American Mathematical Society; Dec2022, Vol. 69 Issue 11, p1942-1955, 14p
Autor:
Xiang-dong Hou
Recently, rational functions of degree three that permute the projective line $\Bbb P^1(\Bbb F_q)$ over a finite field $ \Bbb F_q$ were determined by Ferraguti and Micheli. In the present paper, using a different method, we determine all rational fun
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::186ab12edd9e5e8e7c113534aff0a2f6
http://arxiv.org/abs/2005.07213
http://arxiv.org/abs/2005.07213
Autor:
Xiang-dong Hou
A formula discovered by L. Carlitz in 1935 finds an interesting application in permutation rational functions of finite fields. It allows us to determine all rational functions of degree three that permute the projective line $\Bbb P^1(\Bbb F_q)$ ove
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d52be89019a3fdb61d1e64d6755d6cda
http://arxiv.org/abs/2003.02246
http://arxiv.org/abs/2003.02246
Autor:
Xiang-dong Hou, Daniele Bartoli
Let $p$ be a prime and $n$ be a positive integer, and consider $f_b(X)=X+(X^p-X+b)^{-1}\in \Bbb F_p(X)$, where $b\in\Bbb F_{p^n}$ is such that $\text{Tr}_{p^n/p}(b)\ne 0$. It is known that (i) $f_b$ permutes $\Bbb F_{p^n}$ for $p=2,3$ and all $n\ge 1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::803458e0cb9b2fbffaf3d71707ac61d8
Autor:
Xiang-dong Hou
Publikováno v:
Finite Fields and Their Applications. 54:113-132
Riemann's hypothesis on function fields over a finite field implies the Hasse–Weil bound for the number of zeros of an absolutely irreducible bi-variate polynomial over a finite field. The Hasse–Weil bound has extensive applications in the arithm
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b6da256abf651e7f2f66702761509f94
https://doi.org/10.1016/j.ffa.2018.08.005
https://doi.org/10.1016/j.ffa.2018.08.005