Note on Niederreiter-Xing's propagation rule for linear codes

We present a simple construction of long linear codes from shorter ones. Our approach is related to the product code construction; it generalizes and simplifies substantially the recent "Propagation Rule" by Niederreiter and Xing. Many optimal codes can be produced by our method.


Constructions and bounds on linear error-block codes
LİNG, San; Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-12-01)
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert-Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over F-2. We also study the asymptotic of linear error-block codes. We define the real valued function alpha (q,m,a) (delta), which is an analog of the important real valued function alpha (q) (delta) in the asymptotic theory of classical linear error-correctin...
Modified Redundant Representation for Designing Arithmetic Circuits with Small Complexity
AKLEYLEK, SEDAT; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2012-03-01)
We give a modified redundant representation for designing arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values significantly. Our method works for any finite field. We also give some applications in cryptography.
Improved bounds on Weil sums over Galois rings and homogeneous weights
Ling, San; Özbudak, Ferruh (2006-01-01)
We generalize a recent improvement for the bounds of Weil sums over Galois rings of characteristic p(2) to Galois rings of any characteristic p(l). Our generalization is not as strong as for the case p(2) and we indicate the reason. We give a class of homogeneous weights, including the homogeneous weight defined by Constantinescu and Heise, and we show their relations. We also give an application of our improvements on the homogeneous weights of some codewords.
Optimising a nonlinear utility function in multi-objective integer programming
Ozlen, Melih; Azizoğlu, Meral; Burton, Benjamin A. (2013-05-01)
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective i...
New constructions of entanglement-assisted quantum codes
Allahmadi, A.; AlKenani, A.; Hijazi, R.; Muthana, N.; Özbudak, Ferruh; Solé, P. (2021-01-01)
We present two new constructions of entanglement-assisted quantum error-correcting codes using some fundamental properties of (classical) linear codes in an effective way. The main ideas include linear complementary dual codes and related concatenation constructions. Numerical examples in modest lengths show that our constructions perform better than known constructions in the literature. We also give a proof on a generalization of binary Singleton type bound on entanglement-assisted quantum error-correctin...
Citation Formats
F. Özbudak, “Note on Niederreiter-Xing’s propagation rule for linear codes,” APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, pp. 53–56, 2002, Accessed: 00, 2020. [Online]. Available: