Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula>
Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error correctability wi...
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2025-04-01
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| author | Wei Zhao Weixian Li Hui Chen |
| author_facet | Wei Zhao Weixian Li Hui Chen |
| author_sort | Wei Zhao |
| collection | DOAJ |
| description | Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error correctability within the same code length and code size. Constructing MDS symbol-pair codes is one of the main topics in symbol-pair code research. In this paper, we investigate and characterize the symbol-pair distances of constacyclic codes of arbitrary lengths over finite fields and finite chain rings. Using the characterization of the symbol-pair distance, we present three new classes of MDS symbol-pair constacyclic codes that exhibit large minimum distances. |
| format | Article |
| id | doaj-art-277bae1fcc024f0eb8d808703d862b0a |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-277bae1fcc024f0eb8d808703d862b0a2025-08-20T03:47:48ZengMDPI AGAxioms2075-16802025-04-0114532710.3390/axioms14050327Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula>Wei Zhao0Weixian Li1Hui Chen2School of Mathematics, Foshan University, Foshan 528000, ChinaSchool of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, ChinaSchool of Mathematics, Foshan University, Foshan 528000, ChinaSymbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error correctability within the same code length and code size. Constructing MDS symbol-pair codes is one of the main topics in symbol-pair code research. In this paper, we investigate and characterize the symbol-pair distances of constacyclic codes of arbitrary lengths over finite fields and finite chain rings. Using the characterization of the symbol-pair distance, we present three new classes of MDS symbol-pair constacyclic codes that exhibit large minimum distances.https://www.mdpi.com/2075-1680/14/5/327symbol-pair codesconstacyclic codesfinite fieldsfinite chain rings |
| spellingShingle | Wei Zhao Weixian Li Hui Chen Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> Axioms symbol-pair codes constacyclic codes finite fields finite chain rings |
| title | Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> |
| title_full | Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> |
| title_fullStr | Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> |
| title_full_unstemmed | Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> |
| title_short | Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length <i>np<sup>s</sup></i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> and over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula> |
| title_sort | symbol pair distances of a class of repeated root constacyclic codes of length i np sup s sup i over inline formula math display inline semantics mrow msub mi mathvariant double struck f mi msup mi p mi mi m mi msup msub mrow semantics math inline formula and over inline formula math display inline semantics mrow msub mi mathvariant double struck f mi msup mi p mi mi m mi msup msub mo mo mi u mi msub mi mathvariant double struck f mi msup mi p mi mi m mi msup msub mrow semantics math inline formula |
| topic | symbol-pair codes constacyclic codes finite fields finite chain rings |
| url | https://www.mdpi.com/2075-1680/14/5/327 |
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