Mixed Materials
Non-Invertible-Element Constacyclic Codes over Finite PIRs
| Τίτλος: | Non-Invertible-Element Constacyclic Codes over Finite PIRs |
|---|---|
| Additional Titles: | In this paper we introduce the notion of $λ$-constacyclic codes over finite rings $R$ for arbitary element $λ$ of $R$. We study the non-invertible-element constacyclic codes (NIE-constacyclic codes) over finite principal ideal rings (PIRs). We determine the algebraic structures of all NIE-constacyclic codes over finite chain rings, give the unique form of the sets of the defining polynomials and obtain their minimum Hamming distances. A general form of the duals of NIE-constacyclic codes over finite chain rings is also provided. In particular, we give a necessary and sufficient condition for the dual of an NIE-constacyclic code to be an NIE-constacyclic code. Using the Chinese Remainder Theorem, we study the NIE-constacyclic codes over finite PIRs. Furthermore, we construct some optimal NIE-constacyclic codes over finite PIRs in the sense that they achieve the maximum possible minimum Hamming distances for some given lengths and cardinalities. |
| Συγγραφείς: | Liu, Hongwei, Liu, Jingge |
| Στοιχεία εκδότη: | 2020-11-24 |
| Τύπος εγγράφου: | Mixed materials |
| Όροι ευρετηρίου: | Information Theory, 94B05, 94B60, 94B65, text |
| Σύνδεσμος: | |
| Διαθεσιμότητα: | Open access content. Open access content |
| Other Numbers: | COO oai:arXiv.org:2011.12049 1228447884 |
| Πηγή συνεισφοράς: | CORNELL UNIV From OAIster®, provided by the OCLC Cooperative. |
| Αριθμός Καταχώρησης: | edsoai.on1228447884 |
| Βάση Δεδομένων: | OAIster |
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