| dc.contributor.author |
Şahin, Murat |
|
| dc.contributor.author |
Özimamoğlu, Hayrullah |
|
| dc.date.accessioned |
2022-11-14T06:59:33Z |
|
| dc.date.available |
2022-11-14T06:59:33Z |
|
| dc.date.issued |
2020 |
|
| dc.identifier.citation |
Şahİn, M., & Özİmamoğlu, H. (2020). Additive Toeplitz codes over\begin {document} $\mathbb {F} _ {4} $\end {document}. Advances in Mathematics of Communications, 14(2), 379. |
tr_TR |
| dc.identifier.uri |
http://hdl.handle.net/20.500.11787/7739 |
|
| dc.description.abstract |
In this paper, we introduce additive Toeplitz codes over F4. The
additive Toeplitz codes are a generalization of additive circulant codes over F4.
We find many optimal additive Toeplitz codes (OATC) over F4. These optimal
codes also contain optimal non-circulant codes, so we find new additive codes in
this manner. We provide some theorems to partially classify OATC. Then, we
give a new algorithm that fully classifies OATC by combining these theorems
with Gaborit’s algorithm. We classify OATC over F4 of length up to 13. We
obtain 2 inequivalent optimal additive toeplitz codes (IOATC) that are noncirculant codes of length 5, 92 of length 8, 2068 of length 9, and 39 of length 11.
Moreover, we improve an idea related to quadratic residue codes to construct
optimal and near-optimal additive Toeplitz codes over F4 of length prime p.
We obtain many optimal and near-optimal additive Toeplitz codes for some
primes p from this construction. |
tr_TR |
| dc.language.iso |
eng |
tr_TR |
| dc.relation.isversionof |
10.3934/amc.2020026 |
tr_TR |
| dc.rights |
info:eu-repo/semantics/restrictedAccess |
tr_TR |
| dc.subject |
Additive codes |
tr_TR |
| dc.subject |
Additive circulant codes |
tr_TR |
| dc.subject |
Codes over F4 |
tr_TR |
| dc.subject |
Optimal codes |
tr_TR |
| dc.subject |
Classification |
tr_TR |
| dc.title |
Additive Toeplitz codes over F4 |
tr_TR |
| dc.type |
article |
tr_TR |
| dc.relation.journal |
Advances in Mathematics of Communications |
tr_TR |
| dc.contributor.department |
Nevşehir Hacı Bektaş Veli Üniversitesi/fen-edebiyat fakültesi/matematik bölümü/cebir ve sayılar teorisi anabilim dalı |
tr_TR |
| dc.contributor.authorID |
35963 |
tr_TR |
| dc.contributor.authorID |
0000-0001-7844-1840 |
tr_TR |
| dc.identifier.volume |
14 |
tr_TR |
| dc.identifier.issue |
2 |
tr_TR |
| dc.identifier.startpage |
379 |
tr_TR |
| dc.identifier.endpage |
395 |
tr_TR |