Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.
This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS)matrices.The authors find the exact lower bound of the XOR counts for 4×4 involutory MDS matrices over F2^4.Fur...This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS)matrices.The authors find the exact lower bound of the XOR counts for 4×4 involutory MDS matrices over F2^4.Further,some new structures of 4×4 involutory MDS matrices over F2^mare provided to construct involutory MDS matrices and the authors constructed the lightest4×4 involutory MDS matrices over F2^8so far by using these structures.展开更多
文摘Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.
基金supported in part by the National Natural Science Foundation of China under Grant No.11371356&61877058CAS Project QYZDJ-SSW-SYS022the Strategy Cooperation Project AQ-1701。
文摘This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS)matrices.The authors find the exact lower bound of the XOR counts for 4×4 involutory MDS matrices over F2^4.Further,some new structures of 4×4 involutory MDS matrices over F2^mare provided to construct involutory MDS matrices and the authors constructed the lightest4×4 involutory MDS matrices over F2^8so far by using these structures.
