Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes

Adel Alahmadi (), Patrick Solé and Ramy Taki Eldin
Additional contact information
Adel Alahmadi: Math Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Patrick Solé: I2M, (Aix Marseille Univ., CNRS, Centrale Marseille), 13009 Marseilles, France
Ramy Taki Eldin: Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt

Mathematics, 2023, vol. 11, issue 11, 1-13

Abstract: We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes. This BCH-like bound serves as a foundation for proposing some minimum-distance lower bounds for single-generator quasi-twisted (QT) codes. Associating each QT code with a constacyclic code over an extension field, we obtain the first bound. This is the QT analogue to a result in the literature for quasi-cyclic codes. We point out some weaknesses in this bound and propose a novel bound that takes into account the Chinese remainder theorem approach to QT codes as well as the BCH bound of constacyclic codes. This proposed bound, in contrast to previous bounds in the literature, does not presuppose a specific form of code generator and does not require calculations in any extension field. We illustrate that our bound meets the one in the literature when the code generator adheres to the specific form assumed in that study. Various numerical examples enable us to compare and discuss these bounds.

Keywords: quasi-twisted codes; constacyclic codes; quasi-cyclic codes; BCH bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/11/2539/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/11/2539/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:11:p:2539-:d:1161345

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().