Generalized Gray codes with prescribed ends

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10336924" target="_blank" >RIV/00216208:11320/17:10336924 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.tcs.2017.01.010" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2017.01.010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2017.01.010" target="_blank" >10.1016/j.tcs.2017.01.010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generalized Gray codes with prescribed ends

Popis výsledku v původním jazyce

An n-bit Gray code is a sequence of all n-bit strings such that consecutive strings differ in a single bit. It is well-known that given such strings α, β, an n-bit Gray code between α and β exists iff the Hamming distance d(α,β) of α and β is odd. We generalize this classical result to k pairwise disjoint pairs of n-bit strings αi,βi : if d(αi,βi) is odd for all i and k &lt;n, then the set of all n-bit vectors can be partitioned into k sequences such that the i-th sequence leads from αi to βi and consecutive vectors differ in a single bit. This holds for every n &gt; 1 with one exception in the case that n = k + 1 = 4. Our result is optimal in the sense that for every n &gt; 2 there are n pairwise disjoint pairs of n-bit strings αi,βi with d(αi , βi ) odd for which such sequences do not exist.

Název v anglickém jazyce

Generalized Gray codes with prescribed ends

Popis výsledku anglicky

An n-bit Gray code is a sequence of all n-bit strings such that consecutive strings differ in a single bit. It is well-known that given such strings α, β, an n-bit Gray code between α and β exists iff the Hamming distance d(α,β) of α and β is odd. We generalize this classical result to k pairwise disjoint pairs of n-bit strings αi,βi : if d(αi,βi) is odd for all i and k &lt;n, then the set of all n-bit vectors can be partitioned into k sequences such that the i-th sequence leads from αi to βi and consecutive vectors differ in a single bit. This holds for every n &gt; 1 with one exception in the case that n = k + 1 = 4. Our result is optimal in the sense that for every n &gt; 2 there are n pairwise disjoint pairs of n-bit strings αi,βi with d(αi , βi ) odd for which such sequences do not exist.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA14-10799S" target="_blank" >GA14-10799S: Hyperkrychlové, grafové a hypergrafové struktury</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

—

Svazek periodika

668

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

70-94

Kód UT WoS článku

000400224500005

EID výsledku v databázi Scopus

2-s2.0-85011347260