Improved p-ary codes and sequence families from Galois rings of characteristic p(2)

Date

2006-01-01

Author

LİNG, SAN
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

167
views

0
downloads

This paper explores the applications of a recent bound on some Weil-type exponential sums over Galois rings in the construction of codes and sequences. A family of codes over F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m(D-[D/p2])), where 1 <= D <= p(m/2), is obtained. The bound on this type of exponential sums provides a lower bound for the minimum distance of these codes. Several families of pairwise cyclically distinct p-ary sequences of period p(p(m - 1)) of low correlation are also constructed. They compare favorably with certain known p-ary sequences of period p(m) - 1. Even in the case p = 2, one of these families is slightly larger than the family Q(D) in section 8.8 in [T. Helleseth and P. V. Kumar, Handbook of Coding Theory, Vol. 2, North-Holland, 1998, pp. 1765 - 1853], while they share the same period and the same bound for the maximum nontrivial correlation.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/42175

Journal

SIAM JOURNAL ON DISCRETE MATHEMATICS

DOI

https://doi.org/10.1137/s089548010444506x

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

ON THE k-TH ORDER LFSR SEQUENCE WITH PUBLIC KEY CRYPTOSYSTEMS KIRLAR, Barış Bülent; Cil, Melek (Walter de Gruyter GmbH, 2017-06-01) In this paper, we propose a novel encryption scheme based on the concepts of the commutative law of the k-th order linear recurrences over the finite field F-q for k > 2. The proposed encryption scheme is an ephemeral-static, which is useful in situations like email where the recipient may not be online. The security of the proposed encryption scheme depends on the difficulty of solving some Linear Feedback Shift Register (LFSR) problems. It has also the property of semantic security. For k = 2, we propose ...
On the Krall-type polynomials on q-quadratic lattices Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01) In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
Intelligent analysis of chaos roughness in regularity of walk for a two legged robot Kaygisiz, BH; Erkmen, İsmet; Erkmen, Aydan Müşerref (Elsevier BV, 2006-07-01) We describe in this paper a new approach to the identification of the chaotic boundaries of regular (periodic and quasiperiodic) regions in nonlinear systems, using cell mapping equipped with measures of fractal dimension and rough sets. The proposed fractal-rough set approach considers a state space divided into cells where cell trajectories are determined using cell to cell mapping technique. All image cells in the state space, equipped with their individual fractal dimension are then classified as being ...
On entire rational maps of real surfaces Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01) In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
On quasi-compactness of operator nets on Banach spaces Emelyanov, Eduard (Institute of Mathematics, Polish Academy of Sciences, 2011-01-01) The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Rabiger net (T(lambda))(lambda) is equivalent to quasi-compactness of some operator T(lambda). We prove that strong convergence of a quasi-compact uniform Lotz-Rabiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.

Citation Formats

S. LİNG and F. Özbudak, “Improved p-ary codes and sequence families from Galois rings of characteristic p(2),” SIAM JOURNAL ON DISCRETE MATHEMATICS, pp. 1011–1028, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42175.