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

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 |
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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 |