This paper introduces a suitable Galois group T for a field F of characteristic p,discusses the variation of the Conlon species of the sub-Grecn-ring generated by p-permutationFG-modules under the action of T, and the...This paper introduces a suitable Galois group T for a field F of characteristic p,discusses the variation of the Conlon species of the sub-Grecn-ring generated by p-permutationFG-modules under the action of T, and then proves that the fixed point set of the sub-Green-ring generated by p-permutation modules acted on by T coincides with the sub-Green-ringgenerated by permutation modules.展开更多
This paper design the P-permutation with cryptologic properties beyond certain bound based on BCH code and Goppa code, which is the generalization of the design method utilizing the maximum distance separable （MDS） ...This paper design the P-permutation with cryptologic properties beyond certain bound based on BCH code and Goppa code, which is the generalization of the design method utilizing the maximum distance separable （MDS） code, and presents the novel algorithms to generate the P-permutations with the branch number no less than a preset low bound. The new generation algorithms provide a theoretical basis for automation design of the cryptosystem.展开更多
The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the cha...The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.展开更多
Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is ...Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is stabilized by OB（A）. As applications, someconditions are given for a finite group to be p-supersolvable.展开更多
文摘This paper introduces a suitable Galois group T for a field F of characteristic p,discusses the variation of the Conlon species of the sub-Grecn-ring generated by p-permutationFG-modules under the action of T, and then proves that the fixed point set of the sub-Green-ring generated by p-permutation modules acted on by T coincides with the sub-Green-ringgenerated by permutation modules.
基金Supported by the National Natural Science Foundation of China (60673071, 60970115, 60970116)
文摘This paper design the P-permutation with cryptologic properties beyond certain bound based on BCH code and Goppa code, which is the generalization of the design method utilizing the maximum distance separable （MDS） code, and presents the novel algorithms to generate the P-permutations with the branch number no less than a preset low bound. The new generation algorithms provide a theoretical basis for automation design of the cryptosystem.
基金Supported by the National Natural Science Foundation of China (60970115, 91018008)
文摘The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.
基金The research was partially supported by the National Natural Science Foundation of China （11371237） and a grant of the First-Class Discipline of Universities in Shanghai.
文摘Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is stabilized by OB（A）. As applications, someconditions are given for a finite group to be p-supersolvable.
