In this paper, we show that the Gilbert-Varshamov and the Xing bounds can be improved significantly around two points where these two bounds intersect by nonlinear codes from algebraic curves over finite fields.
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 in-formation rate R = 1/2, by our ...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 in-formation 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.展开更多
In the present paper, we focus on constructive spherical codes. By employing algebraic geometry codes, we give an explicit construction of spherical code sequences. By making use of the idea involved in the proof of t...In the present paper, we focus on constructive spherical codes. By employing algebraic geometry codes, we give an explicit construction of spherical code sequences. By making use of the idea involved in the proof of the Gilbert-Varshamov bound in coding theory, we construct a spherical code sequence in exponential time which meets the best-known asymptotic bound by Shamsiev and Wyner.展开更多
文摘In this paper, we show that the Gilbert-Varshamov and the Xing bounds can be improved significantly around two points where these two bounds intersect by nonlinear codes from algebraic curves over finite fields.
基金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 Chinathe Specialized Research Fund for the Doctoral Program of Higher Education (GrantNo. 20060286006)
文摘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 in-formation 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.
文摘In the present paper, we focus on constructive spherical codes. By employing algebraic geometry codes, we give an explicit construction of spherical code sequences. By making use of the idea involved in the proof of the Gilbert-Varshamov bound in coding theory, we construct a spherical code sequence in exponential time which meets the best-known asymptotic bound by Shamsiev and Wyner.
