Generalized Gray codes with prescribed ends

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Generalized Gray codes with prescribed ends

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

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

Project

<a href="/en/project/GA14-10799S" target="_blank" >GA14-10799S: Hybercubic, graph and hypergraph structures</a><br>

Continuities

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

Publication year

2017

Confidentiality

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

Name of the periodical

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

—

Volume of the periodical

668

Issue of the periodical within the volume

March

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

25

Pages from-to

70-94

UT code for WoS article

000400224500005

EID of the result in the Scopus database

2-s2.0-85011347260