Asymptotic bound on binary self-orthogonal codes |
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Authors: | Yang Ding |
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Affiliation: | (1) Department of Mathematics, Southeast University, Nanjing, 210096, China |
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Abstract: | We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R = 1/2, by our constructive lower bound, the relative minimum distance δ ≈ 0.0595 (for GV bound, δ ≈ 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound. This work was supported by the China Scholarship Council, National Natural Science Foundation of China (Grant No.10571026), the Cultivation Fund of the Key Scientific and Technical Innovation Project of Ministry of Education of China, and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060286006) |
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Keywords: | algebraic geometry codes concatenated codes Gilbert-Varshamov bound Reed-Muller codes self-dual basis self-orthogonal codes |
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