In this paper, we study the p-ary linear code Ck(n, q), q = p , p prime, h ≥ 1, generated by the incidence matrix of points and k-dimensional spaces in PG(n, q). We note that the condition k ≥ n/2 arises in results on the codewords of Ck(n, q). For k ≥ n/2, we link codewords of Ck(n, q)\ Ck(n, q) ⊥ of weight smaller than 2q to k-blocking sets. We first prove that such a k-blocking set is unique...

In this paper, we investigate cyclic code over the ring Fpk + vFpk + v 2 Fpk + ...+ v r Fpk , where v = v, p a prime number, r > 1 and gcd(r, p) = 1, we prove as generalisation of [9] that these codes are principally generated, give generator polynomial and idempotent depending on idempotents over this ring as response to an open problem related in [11]. we also give a gray map and proprieties ...

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 (...

Skew Hadamard designs (4n−1, 2n−1, n−1) are associated to order 4n skew Hadamard matrices in the natural way. We study the codes spanned by their incidence matrices A and by I +A and show that they are self-dual after extension (resp. extension and augmentation) over fields of characteristic dividing n. Quadratic Residues codes are obtained in the case of the Paley matrix. Results on the p−rank...

The construction of cyclic codes can be generalized to so-called ”module θ-codes” using noncommutative polynomials. The product of the generator polynomial g of a self-dual ”module θ-code” and its ”skew reciprocal polynomial” is known to be a noncommutative polynomial of the form X − a, reducing the problem of the computation of all such codes to the resolution of a polynomial system where the ...

Ahstruct-It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial code in this class is shown to hav...

Currently, the existence of an extremal singly even self-dual code of length 24k + 10 is unknown for all nonnegative integers k. In this note, we study singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes. We give some restrictions on the possible weight enumerators of singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes with shadows of minimum weight at least 5 for k = 2, 3, 4, 5. We dis...

In this paper, we study the p-ary linear code C(PG(n, q)), q = p, p prime, h ≥ 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n, q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n, q) and we exclude all possible codewords arising from small linear blocking sets. We also lo...

An extended cyclic code of length 2 m over GF(2) cannot be self-dual for even m. For odd m, the Reed-Muller code [2 m, 2 m1, 2(m + 1)/2] is affine-invariant and selfdual, and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2 m for m = 7 and m = 9. For each odd m, m >i 9, we exhibit a self-dual affine-invariant code of length 2 m ...