Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor | Department of Applied Mathematics | en_US |
| dc.contributor.advisor | Sze, Nung-sing (AMA) | en_US |
| dc.creator | Zheng, Run | - |
| dc.identifier.uri | https://theses.lib.polyu.edu.hk/handle/200/14399 | - |
| dc.language | English | en_US |
| dc.publisher | Hong Kong Polytechnic University | en_US |
| dc.rights | All rights reserved | en_US |
| dc.title | Dimension and Bose distance of certain BCH codes | en_US |
| dcterms.abstract | Error correction codes form the backbone of reliable digital communication and data storage systems. During information transmission, errors are inevitable due to channel noise and interference. Error correction codes provide mathematical frameworks to automatically detect and correct such errors. Their applications span a wide range of critical fields, including communication systems, computer networks, data storage, consumer electronics, and wireless networks. | en_US |
| dcterms.abstract | Bose–Chaudhuri–Hocquenghem (BCH) codes, as a subclass of cyclic codes, play an important role in both theoretical research and practical applications. Their strong error-correcting capability and efficient encoding and decoding algorithms make BCH codes widely used in various domains including telecommunications, memory and storage technologies, and digital electronics. | en_US |
| dcterms.abstract | Although BCH codes have been extensively studied theoretically and are widely used in practice, their key parameters, including dimension, minimum distance, and Bose distance, remain unknown in general. To date, only a limited family of BCH codes has been fully characterized in terms of these parameters. The dimension determines the number of information symbols a BCH code can carry, reflecting its data transmission efficiency. The minimum distance dictates the error-correcting capability of the code, with larger values enabling the correction of more errors. The Bose distance provides a lower bound on the minimum distance and, for certain families of BCH codes, equals it. Therefore, determining these parameters is essential for a deeper understanding and effective application of BCH codes. | en_US |
| dcterms.abstract | Let m be a positive integer, q be a prime power and λ be a divisor of q − 1. In this thesis, we investigate the parameters of q-ary BCH codes of length qm−1/λ, which includes primitive BCH codes as a special case when λ = 1. By deriving some explicit formulas, we determine the dimension and Bose distance of BCH codes with this length qm−1/λ for m ≥ 4 and for designed distances over a significantly wider range of designed distances than previously known. Using these formulas, we identify several optimal codes and linear codes with the best known parameters. | en_US |
| dcterms.extent | ix, 149 pages : illustrations | en_US |
| dcterms.isPartOf | PolyU Electronic Theses | en_US |
| dcterms.issued | 2026 | en_US |
| dcterms.educationalLevel | Ph.D. | en_US |
| dcterms.educationalLevel | All Doctorate | en_US |
| dcterms.LCSH | Error-correcting codes (Information theory) | en_US |
| dcterms.LCSH | Coding theory | en_US |
| dcterms.LCSH | Hong Kong Polytechnic University -- Dissertations | en_US |
| dcterms.accessRights | open access | en_US |
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