A MacWilliams type identity on Lee weight for linear codes over mathbb{F}_2 + umathbb{F}_2^*

In this paper,the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F₂ + uF₂ is determined.As an application of this identity,the authors obtain a MacWilliams type identity on Lee weight for linear codes over F_2^m+ uF_2^m.Furthermore,the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.     

On the Construction of Involutory MDS Matrices over F_(2~m)

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 F_(2~4). Further, some new structures of 4 × 4 involutory MDS matrices over F_(2~m) are provided to construct involutory MDS matrices and the authors constructed the lightest4 × 4 involutory MDS matrices over F_(2~8) so far by using these structures.