{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T16:46:04Z","timestamp":1756572364735,"version":"3.40.5"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> Boolean functions are fundamental bricks in the development of various applications in Cryptography and Coding theory by making benefit from the weights of related Boolean functions (Walsh spectrum). Towards this, the discrete Fourier transform (Walsh\u2013Hadamard) plays a pivotal tool. The work in this paper is dedicated towards the algebraic and numerical degrees, together with the relationship between weights of Boolean function and their Walsh transforms. We introduce Walsh matrices and generalize them to any arbitrary Boolean function. This improves the complexity in computation of Walsh\u2013Hadamard and Fourier transform in certain cases. We also discuss some useful results related to the degree of the algebraic normal form using Walsh\u2013Hadamard transform. <\/jats:p>","DOI":"10.1142\/s0129054122500101","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T01:07:35Z","timestamp":1653440855000},"page":"453-479","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Approach Towards Degree and Walsh-Transform of Boolean Functions"],"prefix":"10.1142","volume":"33","author":[{"given":"Sunil","family":"Kumar","sequence":"first","affiliation":[{"name":"Defence Research and Development Organisation, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8500-9175","authenticated-orcid":false,"given":"Harshdeep","family":"Singh","sequence":"additional","affiliation":[{"name":"Defence Research and Development Organisation, India"}]},{"given":"Gaurav","family":"Mittal","sequence":"additional","affiliation":[{"name":"Defence Research and Development Organisation, India"},{"name":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India"}]}],"member":"219","published-online":{"date-parts":[[2022,5,24]]},"reference":[{"key":"S0129054122500101BIB001","doi-asserted-by":"publisher","DOI":"10.2478\/cait-2018-0018"},{"key":"S0129054122500101BIB004","first-page":"202","volume-title":"International Colloquium on Coding Theory and Applications","author":"Carlet C.","year":"1988"},{"key":"S0129054122500101BIB005","first-page":"131","volume-title":"Discrete Mathematics and Theoretical Computer Science","author":"Carlet C.","year":"2001"},{"key":"S0129054122500101BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.833361"},{"volume-title":"Boolean Functions for Cryptography and Coding Theory","year":"2021","author":"Carlet C.","key":"S0129054122500101BIB007"},{"key":"S0129054122500101BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-46796-3_10"},{"volume-title":"Cryptographic Boolean Functions and Applications","year":"2017","author":"Cusick T. W.","key":"S0129054122500101BIB010"},{"key":"S0129054122500101BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/9361"},{"volume-title":"IEEE International Symposium on Industrial Electronics","year":"2009","author":"Lin Y.","key":"S0129054122500101BIB013"},{"key":"S0129054122500101BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/9789812793430_0023"},{"key":"S0129054122500101BIB015","doi-asserted-by":"publisher","DOI":"10.1109\/IREPGELC.1954.6499441"},{"key":"S0129054122500101BIB017","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1954.1057465"},{"key":"S0129054122500101BIB018","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"S0129054122500101BIB019","doi-asserted-by":"publisher","DOI":"10.3390\/axioms10020042"},{"key":"S0129054122500101BIB020","first-page":"217","volume-title":"Advances in Computer Science and Technology","author":"Wu C.-K.","year":"2016"},{"key":"S0129054122500101BIB021","volume-title":"Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal\/Image Processing","volume":"383","author":"Yarlagadda R. K.","year":"2012"},{"key":"S0129054122500101BIB022","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3102314"},{"key":"S0129054122500101BIB023","doi-asserted-by":"publisher","DOI":"10.1109\/CIS.2010.157"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054122500101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T04:06:37Z","timestamp":1660277197000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0129054122500101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,24]]},"references-count":18,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1142\/S0129054122500101"],"URL":"https:\/\/doi.org\/10.1142\/s0129054122500101","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"type":"print","value":"0129-0541"},{"type":"electronic","value":"1793-6373"}],"subject":[],"published":{"date-parts":[[2022,5,24]]}}}