In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(p, m), with respect to any basis of GR(p, m). These bounds depend on the parameters of GR(p, m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr . Examples are given of Galois ring codes tha...

The performance growth of Islamic commercial banks in Indonesia cannot be said to good enough considering that have been established for 30 years, therefore it is necessary examine what factors can affect the banks. purpose this study determine partial or simultaneous influence Corporate Governance (ICG), Social Responsibility (ICSR) and Islamicity Performance Index (IPI) variables on Financial...

The equivalence between autonomicity and the absence of free variables is a well-known result for linear, shift-invariant and complete behaviors over a field. However, this no longer holds for a behavior that does not satisfy one of those properties. In this paper we consider linear, shift-invariant and complete behaviors over the ring Zpr and study under which conditions such behaviors are aut...

The paper addresses minimality of encoders for basic convolutional codes over Zpr by using a recently developed concept of row reducedness for polynomial matrices over Zpr . It is known in the literature that the McMillan degree of a basic encoder is an upper bound for the minimum number of trellis states, but a general expression is missing. This open problem is solved in this paper. An expand...

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn⋊Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm for the case Zpr ⋊ Zp when p is an odd prime.