On the classification of ideals over \(R[X]/\langle f(X)^{p^s}\rangle\) when \(R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+\cdots+u^n\mathbb{F}_{p^m}\)

DOI10.1007/s12095-022-00620-4zbMath1529.94054MaRDI QIDQ6107455

Mohamed El Hassani Charkani, Jamal Laaouine, B. Boudine

Publication date: 3 July 2023

Published in: Cryptography and Communications (Search for Journal in Brave)

zbMATH Keywords

cyclic codeerror-correcting codescyclotomic polynomial

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomials over finite fields (11T06) Cyclic codes (94B15) Cyclotomy (11T22)

Cites Work

• Unnamed Item
• Repeated-root constacyclic codes of prime power lengths over finite chain rings
• Repeated-root constacyclic codes of length \(\ell p^s\) and their duals
• Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration
• Constacyclic codes of length \(p^s\) over \(\mathbb F_{p^m} + u\mathbb F_{p^m}\)
• Repeated-root constacyclic codes of length
• A note on cyclic codes over \(\mathrm{GR}(p^{2},m)\) of length \(p^{k}\)
• Cyclic codes over \(\text{GR}(p^2,m)\) of length \(p^k\)
• Structure of repeated-root constacyclic codes of length \(3p^s\) and their duals
• Complete classification of repeated-root \(\sigma\)-constacyclic codes of prime power length over \(\mathbb{F}_{p^m} [ u \slash \langle u^3 \rangle \)]
• On the integral ideals of \(R[X\) when \(R\) is a special principal ideal ring]
• Cyclic and negacyclic codes of length \(2p^s\) over \(\mathbb F_{p^m}+u\mathbb F_{p^m}\)
• ON REPEATED-ROOT CONSTACYCLIC CODES OF LENGTH 4p^s
• Calculating cyclotomic polynomials
• Cyclic and Negacyclic Codes Over Finite Chain Rings
• Class Field Theory
• Explicit constructions of cyclic and negacyclic codes of length 3ps over 𝔽pm + u𝔽pm

This page was built for publication: On the classification of ideals over \(R[X]/\langle f(X)^{p^s}\rangle\) when \(R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+\cdots+u^n\mathbb{F}_{p^m}\)