Author(s)

Yong Yang, Wenwei Qiu

School of Mathematics and Information, China West Normal University, Nanchong, China.

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.

Linear Codes, MacWilliams Equations, Weight Distribution, Dual Codes, Deep Holes, Covering Radius

Yang, Y. and Qiu, W. (2023) Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes. Applied Mathematics, 14, 684-695. doi: 10.4236/am.2023.1410040.