Structure of functional codes defined on non-degenerate Hermitian varieties

Edoukou F.A.B.; Ling S.; Xing C.

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Structure of functional codes defined on non-degenerate Hermitian varieties

机译：在非退化厄米品种上定义的功能代码的结构

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We study the functional codes of order h defined by G. Lachaud on a non-degenerate Hermitian variety, by exhibiting a result on divisibility for all the weights of such codes. In the case where the functional code is defined by evaluating quadratic functions on the non-degenerate Hermitian surface, we list the first five weights, describe the geometrical structure of the corresponding quadrics and give a positive answer to a conjecture formulated on this question by Edoukou (2009) [8]. The paper ends with two conjectures. The first is about the divisibility of the weights in the functional codes. The second is about the minimum distance and the distribution of the codewords of the first 2h+1 weights.

机译：我们通过展示非此类厄密变种上的权重结果来研究由G. Lachaud定义的h阶功能码。在通过评估非退化厄米曲面上的二次函数来定义功能代码的情况下，我们列出前五个权重，描述相应二次方程的几何结构，并对由Edoukou对此问题提出的猜想给出肯定答案（2009）[8]。本文以两个猜想结束。首先是功能代码中权重的可除性。第二个是关于最小距离和前2h + 1个权重的码字的分布。

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《Journal of Combinatorial Theory, Series A》 |2011年第8期|共9页
作者
Edoukou F.A.B.; Ling S.; Xing C.;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Divisor of a code; Functional codes; Hermitian surface; Hermitian variety; Weight;

机译：代码的除数;功能代码;埃尔米特表面;埃尔米特变种;重量;

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1. 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
2. Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in mathbbP4(mathbbF_q){mathbb{P}^{4}(mathbb{F}_q)} [J] . Frédéric A. B. Edoukou Designs, Codes and Cryptography . 2009,第1期

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}}
3. On the functional codes defined by quadrics and Hermitian varieties [J] . D. Bartoli, M. De Boeck, S. Fanali, Designs, Codes and Crytography . 2014,第1期

机译：关于二次和Hermitian变体定义的功能代码
4. On the structure of Hermitian codes and decoding for burst errors [C] . Ren, J. Global Telecommunications Conference, 2003. GLOBECOM '03. IEEE . 2003

机译：埃尔米特码的结构和突发错误的解码
5. Defining genetic elements and protein structure by selecting functional sequences from random DNA [D] . Oliphant, Arnold R. 1989

机译：通过从随机DNA中选择功能序列来定义遗传元素和蛋白质结构
6. Quantization of wave equations and hermitian structures in partial differential varieties [O] . S. M. Paneitz, I. E. Segal 1980

机译：偏微分品种中波动方程和厄米结构的量化
7. The small weight codewords of the functional codes associated to non-singular hermitian varieties [O] . Edoukou Frederic AB, Hallez Anja, Rodier Francois, 2010

机译：与非奇异厄米特种类相关的功能代码的小权重码字

Structure of functional codes defined on non-degenerate Hermitian varieties

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