Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in mathbbP4(mathbbF<sub>q</sub>){mathbb{P}^{4}(mathbb{F}_q)}

Frédéric A. B. Edoukou

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Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in mathbbP4(mathbbF_q){mathbb{P}^{4}(mathbb{F}_q)}

机译：在mathbbP 4 （mathbbF _{q ）{mathbb {P} ^ {4}（mathbb {F} _q）中的非退化厄米变体上以2级形式定义的代码}}

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We study the functional codes of second order on a non-degenerate Hermitian variety X Ì mathbbP4(mathbbF_q){mathcal{X} subset {mathbb{P}}^4(mathbb{F}_q)} as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of X{mathcal{X}} . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety X Ì mathbbP4(mathbbF_q){mathcal{X} subset{mathbb{P}}^4(mathbb{F}_q)} . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular Hermitian variety X Ì mathbbPN(mathbbF_q){mathcal{X} subset {mathbb{P}}^N(mathbb{F}_q)} .

机译：我们研究了非退化厄米变种XÌmathbbP 4 （mathbbF _{q ）{mathcal {X}子集{mathbb {P}} ^上的二阶功能代码。 G. Lachaud定义的4（mathbb {F} _q）}。我们为X {mathcal {X}}的二次截面的点数提供了最佳边界。我们列出前五个权重，描述相应的码字并计算其数量。本文以两个猜想结束。第一个是关于非奇异的Hermitian变种XÌmathbbP 4 （mathbbF _{q ）{mathcal {X}子集{mathbb {P}} ^ 4（mathbb {F} _q）}。第二个是关于非奇异Hermitian变种XÌmathbbP N （mathbbF _{q ）{mathcal上二阶功能码的前五个权重的代码字的分布{X}个子集{mathbb {P}} ^ N（mathbb {F} _q）}。}}}

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《Designs, Codes and Cryptography》 |2009年第1期|p.135-146|共12页
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Frédéric A. B. Edoukou;
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1. Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in P~4(F_q) [J] . Frederic A. B. Edoukou Designs, Codes and Crytography . 2009,第1期

机译：P〜4（F_q）中非退化厄米变体上以2度形式定义的代码
2. Structure of functional codes defined on non-degenerate Hermitian varieties [J] . Edoukou F.A.B., Ling S., Xing C. Journal of Combinatorial Theory, Series A . 2011,第8期

机译：在非退化厄米品种上定义的功能代码的结构
3. Codes defined by forms of degree 2 on Hermitian surfaces and Sorensen's conjecture [J] . Frederic A.B. Edoukou Finite fields and their applications . 2007,第3期

机译：由Hermitian曲面上的2度形式和Sorensen猜想定义的代码
4. Performance Comparison between Hermitian codes and Shortened Non-binary BCH codes [C] . Mubarak Jibril, Martin Tomlinson, Mohammed Zaki Ahmed, International Conference on Microwaves, Communications, Antennas and Electronic Systems . 2009

机译：隐士代码与缩短非二元BCH代码的性能比较
5. Space Takes Time: Concentration Dependent Output Codes from Primary Olfactory Networks Rapidly Provide Additional Information at Defined Discrimination Thresholds [O] . Kevin C. Daly, Samual Bradley, Phillip D. Chapman, 1973

机译：空间需要时间：来自主要嗅觉网络的浓度相关输出代码可在定义的歧视阈值下快速提供其他信息
6. Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture [O] . Edoukou Frédéric A.B. 2007

机译：由Hermitian曲面上的2度形式和Sørensen猜想定义的代码

Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in mathbbP4(mathbbFq){mathbb{P}^{4}(mathbb{F}_q)}

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Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in mathbbP4(mathbbF_q){mathbb{P}^{4}(mathbb{F}_q)}