Reverse-free codes and permutations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10108507" target="_blank" >RIV/00216208:11320/11:10108507 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S1571065311001314" target="_blank" >http://www.sciencedirect.com/science/article/pii/S1571065311001314</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.endm.2011.09.062" target="_blank" >10.1016/j.endm.2011.09.062</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reverse-free codes and permutations

Popis výsledku v původním jazyce

Two codewords (a1,...,ak) and (b1,...,bk) form a reverse-free pair if (ai,aj) is not equal to (bj,bi) whenever 1{i,j{k are indices such that ai is not equal to aj. In a reverse-free code, each pair of codewords is reverse-free. The maximum size of a reverse-free code with codewords of length k and an n-element alphabet is denoted by F'(n,k). Let F(n,k) denote the maximum size of a reverse-free code with all codewords consisting of distinct entries. We determine F'(n,3) and F(n,3) exactly whenever n is apower of 3, and asymptotically for other values of n. We prove non-trivial bounds for F(n,k) and F'(n,k) for general k and for other related functions as well. Using VC-dimension of a matrix, we determine the order of magnitude of F'(n,k) for n fixed and k tending to infinity.

Název v anglickém jazyce

Reverse-free codes and permutations

Popis výsledku anglicky

Two codewords (a1,...,ak) and (b1,...,bk) form a reverse-free pair if (ai,aj) is not equal to (bj,bi) whenever 1{i,j{k are indices such that ai is not equal to aj. In a reverse-free code, each pair of codewords is reverse-free. The maximum size of a reverse-free code with codewords of length k and an n-element alphabet is denoted by F'(n,k). Let F(n,k) denote the maximum size of a reverse-free code with all codewords consisting of distinct entries. We determine F'(n,3) and F(n,3) exactly whenever n is apower of 3, and asymptotically for other values of n. We prove non-trivial bounds for F(n,k) and F'(n,k) for general k and for other related functions as well. Using VC-dimension of a matrix, we determine the order of magnitude of F'(n,k) for n fixed and k tending to infinity.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů