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...

We study the dual linear code of points and generators on a nonsingular Hermitian variety H(2n + 1, q2). We improve the earlier results for n = 2, we solve the minimum distance problem for general n, we classify the n smallest types of code words and we characterize the small weight code words as being a linear combination of these n types.

Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communication and storage systems. However, their weight distributions are known only for a few cases mainly on the codes with one or two nonzeros. In this paper, the weight distributions of two classes of cyclic codes with three or four nonzeros are determ...

We introduce a new approach which facilitates the calculation of the covering radius of a binary linear code. It is based on determining the normalized covering radius p. For codes of fixed dimension we give upper and lower bounds on p that arc reasonably close. As an application, an explicit formula is given for the covering radius of an arbitrary code of dimension <4. This approach also sheds...

Keywords: Linear codes MDS-codes AMS Subject classiication (1985) 94B05 Summary: We give several bounds for the length, dimension or minimum distance of linear block codes whose dimension equals the minimum distance of their dual codes. Zusammenfassung: Wir geben verschiedene Schranken f ur die L ange, die Dimension und den Minimalabstand linearer Blockcodes, deren Dimension gleich dem Mini-mal...

A condition on the weight of a codeword of a linear code is obtained using polynomials over the p-adic numbers. This condition is obtained by proving a bound on the size of a t-fold blocking set of hyperplanes in a finite affine space.

In the present paper, the focus is on the evaluation of steel dual-system frame buildings using four main types of structural analysis (Linear Static, Linear Dynamic, Nonlinear Static and Nonlinear Dynamic Analyses) with regard to "Seismic Rehabilitation Code for Existing Buildings in Iran" (based on FEMA 273 and 356) where the first two authors of the article tend to follow the previous work (...

Each positive increasing integer sequence {an}n≥0 can serve as a numeration system to represent each non-negative by means of suitable coefficient strings. We analyse the case k-generalized Fibonacci sequences leading binary strings avoiding 1k. prove bijection between set such length n and Sn+1(321,312,23…(k+1)1) which is subset symmetric group Sn+1 permutations n+1 permutation patterns 321,31...