<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study properties of differences of finite binary sequences with a fixed number of ones, treated as binary numbers from ℤ (2<sup>m</sup>).We show that any binary sequence consisting of m terms (except of the sequence (1, 0, . . . , 0)) can be presented as a difference of two sequences having exactly n ones, whenever <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-1.jpg"></inline-graphic></alternatives></inline-formula>.</p></abstract>

We study properties of differences of finite binary sequences with a fixed number of ones, treated as binary numbers from ℤ (2m).We show that any binary sequence consisting of m terms (except of the sequence (1, 0, . . . , 0)) can be presented as a difference of two sequences having exactly n ones, whenever .

Some Algebraic Properties of Finite Binary Sequences

Faculty of Mathematics and Computer Sciences Lodz University ul. Stefana Banacha 22 PL–90-238 Łódź POLAND

Institute of Mathematics Lodz University of Technology ul. Wólczańska 215 PL–93-005 Łódź POLAND

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Some Algebraic Properties of Finite Binary Sequences"}

We study properties of differences of finite binary sequences with a fixed number of ones, treated as binary numbers from ℤ (2m).We show that any binary...

Some Algebraic Properties of Finite Binary Sequences

Publié en ligne: 04 août 2016

Pages: 93 - 104

Reçu: 21 oct. 2015

DOI: https://doi.org/10.1515/tmmp-2016-0008

Mots clés
binary sequence, statistic density, difference cover, k-sum

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Some Algebraic Properties of Finite Binary Sequences

Publié en ligne: 04 août 2016

Pages: 93 - 104

Reçu: 21 oct. 2015

DOI: https://doi.org/10.1515/tmmp-2016-0008

Mots clésbinary sequence, statistic density, difference cover, k-sum

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
binary sequence, statistic density, difference cover, k-sum