| 1. | Dual coding hybrid genetic algorithm for optimal schedule of pumping stations in multi - sources water injection system
多源注水系统泵站优化调度的双重编码混合遗传算法 |
| 2. | Absolute minimal trellis complexities of extended codes and their dual codes of two types of linear block codes whose code length is odd are given
给出了两类奇数码长线性分组码的扩展码及其对偶码的绝对最小网格图复杂度。 |
| 3. | All [ 54 , 27 , 10 ] binary self - dual codes with an automorphism of order 7 are enumerated , and up to equivalence , there are 533 such codes
摘要给出了有7阶自同构的二元自对偶编码[ 54 , 27 , 10 ]的生成矩阵，并且证明了在等价情况下，总共有533种这样的编码。 |
| 4. | From these conclusions some results are obtained on absolute minimal trellis complexities of extended primitive bch codes and their dual codes of primitive bch codes
由此得出有关本原bch码的扩展bch码及其对偶码绝对最小网格图复杂度的若干结论。 |
| 5. | “ this is one of the strongest predictors of rates of protein evolution known , indicating that this dual coding role is vastly more influential than previously believed
“这是测定目前已知蛋白进化率的最好的一个工具，双重功能基因的作用范围远比以前人们所认识的还要广泛。 ” |
| 6. | We define a frobenius map over galois , trace codes and subring subcode . we prove the trace of dual codes over galois is the dual codes of subring subcode . all the results are very important for the study of the error correcting codes over rings
第四，作者在galois环gr ( q ~ m )上定义了frobenius映射，并在该环上定义了迹码和子环子码的概念，得到了galois环上的一个码的对偶码的迹码是该码的子环子码的对偶码。 |
| 7. | - the trace representation and the 2 - adic representation for the dual of the quaternary goethals code are given , and its binary image is proved to be the formal dual of the binary goethals code . - the generalized macwilliams identities are given for the support weight distribution of a quaternary linear code with type 4k and that of its dual code
给出了四元goethals码的对偶码的迹表示及2 - adic表示，并证明了它在gray映射下的二元像是二元goethals码的形式对偶码；从而可以将对非线性码二元goethals码及其形式对偶码的研究转化为对四元线性码的研究； 3 |
| 8. | At last , by using the factorization properties of cyclotomic polynmials on finite fields and the construction characteristic of cyclic codes , we present the relation of the period distribution of cyclic codes and the period distribution of their dual codes , establish the explicit formula for the number of the codewords without inner - period of the cyclic codes and their dual codes , find the method for computing the dimension and the period distribution of narrow - sense primitive bch codes , and study the inverse question of period distribution of cyclic codes
最后，利用有限域上分圆多项式的分解特性和循环码的构造特点，揭示了循环码的周期分布与其对偶码周期分布之间的内在联系，确定了一般循环码及其对偶码内无内周期码字的精确计数公式，决定了狭义本原bch码的维数与周期分布，讨论了循环码周期分布的反问题。 |
