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Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes
School of Mathematics and Information, China West Normal University, Nanchong, China
School of Mathematics and Information, China West Normal University, Nanchong, China
- 1 School of Mathematics and Information, China West Normal University, Nanchong, China
- 2 School of Mathematics and Information, China West Normal University, Nanchong, China
Applied Mathematics·Volume 14 (2023)·Pages 684–695·Published 7 October 2023·DOI10.4236/am.2023.1410040
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Abstract
Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.
KeywordsLinear CodesMacWilliams EquationsWeight DistributionDual CodesDeep HolesCovering Radius
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