High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes
Cross parity codes are mostly used as 2-dimensional codes, and sometimes as 3-dimensional codes. We argue that higher dimensions can help to reduce the number of parity bits, and thus deserve further investigation. As a start, we investigate parities from <inline-formula><math xmlns="h...
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2025-04-01
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| author | Jörg Keller |
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| description | Cross parity codes are mostly used as 2-dimensional codes, and sometimes as 3-dimensional codes. We argue that higher dimensions can help to reduce the number of parity bits, and thus deserve further investigation. As a start, we investigate parities from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional hyperplanes in <i>d</i>-dimensional parity codes, instead of parities from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional hyperplanes as usual. |
| format | Article |
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| institution | OA Journals |
| issn | 2073-431X |
| language | English |
| publishDate | 2025-04-01 |
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| spelling | doaj-art-8e9a34c80b8b428189151bcb9a043fca2025-08-20T02:33:42ZengMDPI AGComputers2073-431X2025-04-0114516110.3390/computers14050161High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional HyperplanesJörg Keller0Faculty of Mathematics and Computer Science, FernUniversität in Hagen, 58084 Hagen, GermanyCross parity codes are mostly used as 2-dimensional codes, and sometimes as 3-dimensional codes. We argue that higher dimensions can help to reduce the number of parity bits, and thus deserve further investigation. As a start, we investigate parities from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional hyperplanes in <i>d</i>-dimensional parity codes, instead of parities from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional hyperplanes as usual.https://www.mdpi.com/2073-431X/14/5/161cross parity codeserror-correction block codescode optimization |
| spellingShingle | Jörg Keller High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes Computers cross parity codes error-correction block codes code optimization |
| title | High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes |
| title_full | High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes |
| title_fullStr | High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes |
| title_full_unstemmed | High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes |
| title_short | High-Dimensional Cross Parity Codes and Parities from Lower Than (<i>d</i> − 1)-Dimensional Hyperplanes |
| title_sort | high dimensional cross parity codes and parities from lower than i d i 1 dimensional hyperplanes |
| topic | cross parity codes error-correction block codes code optimization |
| url | https://www.mdpi.com/2073-431X/14/5/161 |
| work_keys_str_mv | AT jorgkeller highdimensionalcrossparitycodesandparitiesfromlowerthanidi1dimensionalhyperplanes |