{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:30:04Z","timestamp":1747189804411,"version":"3.40.5"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p>The problem \u201cGiven a Boolean function [Formula: see text] of [Formula: see text] variables by its truth table vector. Find (if exists) a vector [Formula: see text] of maximal (or minimal) weight, such that [Formula: see text].\u201d is considered here. It is closely related to the problem of computing the algebraic degree of Boolean functions which is an important cryptographic parameter. To solve this problem efficiently, we explore the orders of the vectors of the [Formula: see text]-dimensional Boolean cube [Formula: see text] according to their weights. The notion of \u201c[Formula: see text]th layer\u201d of [Formula: see text] is involved in the definition and examination of the \u201cweight order\u201d relation. It is compared with the known relation \u201cprecedes\u201d. Several enumeration problems concerning these relations are solved and the relevant notes were added to three sequences in the on-line encyclopedia of integer sequences (OEIS). One special weight order is defined and examined in detail. In it, the lexicographic order is a second criterion for an ordinance of the vectors of equal weights. So a total order called weight-lexicographic order (WLO) is obtained. Two algorithms for generating the WLO sequence and two algorithms for generating the characteristic vectors of the layers are proposed. The results obtained by them were used in creating two new sequences: A294648 and A305860 in the OEIS. Two algorithms for solving the problem considered are developed \u2014 the first one works in a byte-wise manner and uses the WLO sequence, and the second one works in a bitwise manner and uses the characteristic vector as masks. The experimental results from numerous tests confirm the efficiency of these algorithms. Other applications of the obtained algorithms are also discussed \u2014 when representing, generating and ranking other combinatorial objects.<\/jats:p>","DOI":"10.1142\/s179383092150021x","type":"journal-article","created":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T06:54:01Z","timestamp":1599720841000},"page":"2150021","source":"Crossref","is-referenced-by-count":1,"title":["Some problems and algorithms related to the weight order relation on the n-dimensional Boolean cube"],"prefix":"10.1142","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2503-5325","authenticated-orcid":false,"given":"Valentin","family":"Bakoev","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, \u201cSt. Cyril and St. Methodius\u201d University, 2 Theodosi Tarnovski Str., Veliko Tarnovo 5000, Bulgaria"}]}],"member":"219","published-online":{"date-parts":[[2020,10,24]]},"reference":[{"volume-title":"The Design and Analysis of Computer Algorithms","year":"1974","author":"Aho A. 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