Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287824620> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W4287824620 abstract "We consider rational functions of the form $V(x)/U(x)$, where both $V(x)$ and $U(x)$ are polynomials over the finite field $mathbb{F}_q$. Polynomials that permute the elements of a field, called {it permutation polynomials ($PPs$)}, have been the subject of research for decades. Let ${mathcal P}^1(mathbb{F}_q)$ denote $mathbb{Z}_q cup {infty}$. If the rational function, $V(x)/U(x)$, permutes the elements of ${mathcal P}^1(mathbb{F}_q)$, it is called a {em permutation rational function (PRf)}. Let $N_d(q)$ denote the number of PPs of degree $d$ over $mathbb{F}_q$, and let $N_{v,u}(q)$ denote the number of PRfs with a numerator of degree $v$ and a denominator of degree $u$. It follows that $N_{d,0}(q) = N_d(q)$, so PRFs are a generalization of PPs. The number of monic degree 3 PRfs is known [11]. We develop efficient computational techniques for $N_{v,u}(q)$, and use them to show $N_{4,3}(q) = (q+1)q^2(q-1)^2/3$, for all prime powers $q le 307$, $N_{5,4}(q) > (q+1)q^3(q-1)^2/2$, for all prime powers $q le 97$, and $N_{4,4}(p) = (p+1)p^2(p-1)^3/3$, for all primes $p le 47$. We conjecture that these formulas are, in fact, true for all prime powers $q$. Let $M(n,D)$ denote the maximum number of permutations on $n$ symbols with pairwise Hamming distance $D$. Computing improved lower bounds for $M(n,D)$ is the subject of much current research with applications in error correcting codes. Using PRfs, we obtain significantly improved lower bounds on $M(q,q-d)$ and $M(q+1,q-d)$, for $d in {5,7,9}$." @default.
- W4287824620 created "2022-07-26" @default.
- W4287824620 creator A5035977878 @default.
- W4287824620 creator A5039604569 @default.
- W4287824620 creator A5061707475 @default.
- W4287824620 creator A5074694552 @default.
- W4287824620 creator A5077091406 @default.
- W4287824620 date "2020-03-23" @default.
- W4287824620 modified "2023-09-24" @default.
- W4287824620 title "Improved Lower Bounds for Permutation Arrays Using Permutation Rational Functions" @default.
- W4287824620 doi "https://doi.org/10.48550/arxiv.2003.10072" @default.
- W4287824620 hasPublicationYear "2020" @default.
- W4287824620 type Work @default.
- W4287824620 citedByCount "0" @default.
- W4287824620 crossrefType "posted-content" @default.
- W4287824620 hasAuthorship W4287824620A5035977878 @default.
- W4287824620 hasAuthorship W4287824620A5039604569 @default.
- W4287824620 hasAuthorship W4287824620A5061707475 @default.
- W4287824620 hasAuthorship W4287824620A5074694552 @default.
- W4287824620 hasAuthorship W4287824620A5077091406 @default.
- W4287824620 hasBestOaLocation W42878246201 @default.
- W4287824620 hasConcept C114614502 @default.
- W4287824620 hasConcept C118615104 @default.
- W4287824620 hasConcept C121332964 @default.
- W4287824620 hasConcept C184992742 @default.
- W4287824620 hasConcept C202444582 @default.
- W4287824620 hasConcept C21308566 @default.
- W4287824620 hasConcept C24890656 @default.
- W4287824620 hasConcept C2775997480 @default.
- W4287824620 hasConcept C2780990831 @default.
- W4287824620 hasConcept C33923547 @default.
- W4287824620 hasConcept C75190567 @default.
- W4287824620 hasConcept C77926391 @default.
- W4287824620 hasConcept C9652623 @default.
- W4287824620 hasConceptScore W4287824620C114614502 @default.
- W4287824620 hasConceptScore W4287824620C118615104 @default.
- W4287824620 hasConceptScore W4287824620C121332964 @default.
- W4287824620 hasConceptScore W4287824620C184992742 @default.
- W4287824620 hasConceptScore W4287824620C202444582 @default.
- W4287824620 hasConceptScore W4287824620C21308566 @default.
- W4287824620 hasConceptScore W4287824620C24890656 @default.
- W4287824620 hasConceptScore W4287824620C2775997480 @default.
- W4287824620 hasConceptScore W4287824620C2780990831 @default.
- W4287824620 hasConceptScore W4287824620C33923547 @default.
- W4287824620 hasConceptScore W4287824620C75190567 @default.
- W4287824620 hasConceptScore W4287824620C77926391 @default.
- W4287824620 hasConceptScore W4287824620C9652623 @default.
- W4287824620 hasLocation W42878246201 @default.
- W4287824620 hasOpenAccess W4287824620 @default.
- W4287824620 hasPrimaryLocation W42878246201 @default.
- W4287824620 hasRelatedWork W11943365 @default.
- W4287824620 hasRelatedWork W14429072 @default.
- W4287824620 hasRelatedWork W18299066 @default.
- W4287824620 hasRelatedWork W31293336 @default.
- W4287824620 hasRelatedWork W39641425 @default.
- W4287824620 hasRelatedWork W44748917 @default.
- W4287824620 hasRelatedWork W7422309 @default.
- W4287824620 hasRelatedWork W7780975 @default.
- W4287824620 hasRelatedWork W7978484 @default.
- W4287824620 hasRelatedWork W7758734 @default.
- W4287824620 isParatext "false" @default.
- W4287824620 isRetracted "false" @default.
- W4287824620 workType "article" @default.