On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12
Almost Difference Sets have extensive applications in coding theory and cryptography. In this study, we introduce new constructions of Almost Difference Sets derived from cyclotomic classes of order 12 in the finite field GF(q), where q is a prime satisfying the form q=12n+1 for positive integers n...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Center for Policy, Research and Development Studies
2023-12-01
|
| Series: | Recoletos Multidisciplinary Research Journal |
| Subjects: | |
| Online Access: | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/1708 |
| _version_ | 1827391214675034112 |
|---|---|
| author | Benedict Estrella |
| author_facet | Benedict Estrella |
| author_sort | Benedict Estrella |
| collection | DOAJ |
| description | Almost Difference Sets have extensive applications in coding theory and cryptography. In this study, we introduce new constructions of Almost Difference Sets derived from cyclotomic classes of order 12 in the finite field GF(q), where q is a prime satisfying the form q=12n+1 for positive integers n ≥ 1 and q < 1000. We show that a single cyclotomic class of order 12 (with and without zero) can form an almost difference set. Additionally, we successfully construct almost difference sets using unions of cyclotomic classes of order 12, both for even and odd values of n. To accomplish this, an exhaustive computer search employing Python was conducted. The method involved computing unions of two cyclotomic classes up to eleven classes and assessing the presence of almost difference sets. Finally, we classify the resulting almost difference sets with the same parameters up to equivalence and complementation. |
| first_indexed | 2024-03-08T17:08:10Z |
| format | Article |
| id | doaj.art-0138c4b74dfa472a95b99994be3ef982 |
| institution | Directory Open Access Journal |
| issn | 2423-1398 2408-3755 |
| language | English |
| last_indexed | 2024-03-08T17:08:10Z |
| publishDate | 2023-12-01 |
| publisher | Center for Policy, Research and Development Studies |
| record_format | Article |
| series | Recoletos Multidisciplinary Research Journal |
| spelling | doaj.art-0138c4b74dfa472a95b99994be3ef9822024-01-04T04:02:13ZengCenter for Policy, Research and Development StudiesRecoletos Multidisciplinary Research Journal2423-13982408-37552023-12-01112576710.32871/rmrj2311.02.06On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12Benedict Estrella0https://orcid.org/0000-0002-3159-293XBulacan State University, Bulacan, PhilippinesAlmost Difference Sets have extensive applications in coding theory and cryptography. In this study, we introduce new constructions of Almost Difference Sets derived from cyclotomic classes of order 12 in the finite field GF(q), where q is a prime satisfying the form q=12n+1 for positive integers n ≥ 1 and q < 1000. We show that a single cyclotomic class of order 12 (with and without zero) can form an almost difference set. Additionally, we successfully construct almost difference sets using unions of cyclotomic classes of order 12, both for even and odd values of n. To accomplish this, an exhaustive computer search employing Python was conducted. The method involved computing unions of two cyclotomic classes up to eleven classes and assessing the presence of almost difference sets. Finally, we classify the resulting almost difference sets with the same parameters up to equivalence and complementation.https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/1708almost difference setcyclotomic classcyclotomyunion |
| spellingShingle | Benedict Estrella On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12 Recoletos Multidisciplinary Research Journal almost difference set cyclotomic class cyclotomy union |
| title | On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12 |
| title_full | On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12 |
| title_fullStr | On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12 |
| title_full_unstemmed | On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12 |
| title_short | On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12 |
| title_sort | on some new almost difference sets constructed from cyclotomic classes of order 12 |
| topic | almost difference set cyclotomic class cyclotomy union |
| url | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/1708 |
| work_keys_str_mv | AT benedictestrella onsomenewalmostdifferencesetsconstructedfromcyclotomicclassesoforder12 |