Majority Logic Decoding of Affine Grassmann Codes Over Nonbinary Fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911053792673792 |
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| author | González, Fernando Piñero Singh, Prasant Yadav, Rohit |
| author_facet | González, Fernando Piñero Singh, Prasant Yadav, Rohit |
| contents | In this article, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with respect to a fixed coordinate. By leveraging the automorphism groups of these codes, we generate a set of orthogonal parity checks for each coordinate. Using these parity checks, we perform majority logic decoding to correct a large number of errors in affine Grassmann codes. The order of error correction capability and the complexity of this decoder for affine Grassmann codes are the same as those of the majority logic decoder for Grassmann codes proposed in [BS21]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Majority Logic Decoding of Affine Grassmann Codes Over Nonbinary Fields González, Fernando Piñero Singh, Prasant Yadav, Rohit Information Theory 14M15, 14G50, 94B27, 94B35 In this article, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with respect to a fixed coordinate. By leveraging the automorphism groups of these codes, we generate a set of orthogonal parity checks for each coordinate. Using these parity checks, we perform majority logic decoding to correct a large number of errors in affine Grassmann codes. The order of error correction capability and the complexity of this decoder for affine Grassmann codes are the same as those of the majority logic decoder for Grassmann codes proposed in [BS21]. |
| title | Majority Logic Decoding of Affine Grassmann Codes Over Nonbinary Fields |
| topic | Information Theory 14M15, 14G50, 94B27, 94B35 |
| url | https://arxiv.org/abs/2507.09741 |