Shi, Minjia and Helleseth, Tor and Özbudak, Ferruh (2023) Covering radius of generalized Zetterberg type codes over finite fields of odd characteristic. IEEE Transactions on Information Theory . ISSN 0018-9448 (Print) 1557-9654 (Online) Published Online First https://dx.doi.org/10.1109/TIT.2023.3296754
There is a more recent version of this item available.
Official URL: https://dx.doi.org/10.1109/TIT.2023.3296754
Abstract
Let F q0 be a finite field of odd characteristic. For an integer s ≥ 1, let C s (q0) be the generalized Zetterberg code of length q s 0 + 1 over F q0 . If s is even, then we prove that the covering radius of C s (q0) is 3. Put q = q s 0 . If s is odd and q ≢ 7 mod 8, then we present an explicit lower bound N 1 (q0) so that if s ≥ N 1 (q0), then the covering radius of C s (q0) is 3. We also show that the covering radius of C 1 (q0) is 2. Moreover we study some cases when s is an odd integer with 3 ≤ s ≤ N 1 (q0) and, rather unexpectedly, we present concrete examples with covering radius 2 in that range. We introduce half generalized Zetterberg codes of length (q s 0 + 1)/2 if q ≡ 1 mod 4. Similarly we introduce twisted half generalized Zetterberg codes of length (q s 0 + 1)/2 if q ≡ 3 mod 4. We show that the same results hold for the half and twisted half generalized Zetterberg codes.
Item Type: | Article |
---|---|
Uncontrolled Keywords: | algebraic curve; Codes; covering radius; Decoding; finite field; Indexes; Informatics; Linear codes; Parity check codes; Testing; Zetterberg codes |
Divisions: | Faculty of Engineering and Natural Sciences |
Depositing User: | Ferruh Özbudak |
Date Deposited: | 07 Aug 2023 21:23 |
Last Modified: | 07 Aug 2023 21:23 |
URI: | https://research.sabanciuniv.edu/id/eprint/47578 |
Available Versions of this Item
- Covering radius of generalized Zetterberg type codes over finite fields of odd characteristic. (deposited 07 Aug 2023 21:23) [Currently Displayed]