Constructing linear unequal error protection codes from algebraic curves

We show that the concept of "generalized algebraic geometry codes" which was recently introduced by Xing, Niederreiter, and Lam gives a natural framework for constructing linear unequal error protection codes.


Search for Boolean functions with excellent profiles in the rotation symmetric class
Kavut, Selcuk; Maitra, Subhamoy; Yucel, Melek D. (Institute of Electrical and Electronics Engineers (IEEE), 2007-05-01)
For the first time Boolean functions on 9 variables having nonlinearity 241 are discovered, that remained as an open question in literature for almost three decades. Such functions are found by heuristic search in the space of rotation symmetric Boolean functions (RSBFs). This shows that there exist Boolean functions on n (odd) variables having non, linearity > 2(n-1) - 2 (n-1/2) if and only if n > 7. Using similar search technique, balanced Boolean functions on 9, 10, and 11 variables are attained having a...
Cyclic codes and reducible additive equations
Guneri, Cem; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2007-02-01)
We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocqu...
An improvement on the bounds of Weil exponential sums over Gallois rings with some applications
Ling, S; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2004-10-01)
We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum dista...
On Linear Complementary Pairs of Codes
CARLET, Claude; Guneri, Cem; Özbudak, Ferruh; Ozkaya, Buket; SOLE, Patrick (Institute of Electrical and Electronics Engineers (IEEE), 2018-10-01)
We study linear complementary pairs (LCP) of codes (C, D), where both codes belong to the same algebraic code family. We especially investigate constacyclic and quasicyclic LCP of codes. We obtain characterizations for LCP of constacyclic codes and LCP of quasi-cyclic codes. Our result for the constacyclic complementary pairs extends the characterization of linear complementary dual (LCD) cyclic codes given by Yang and Massey. We observe that when C and I) are complementary and constacyclic, the codes C and...
Systematic authentication codes using additive polynomials
Özbudak, Ferruh (Springer Science and Business Media LLC, 2008-12-01)
Using additive polynomials related to some curves over finite fields, we construct two families of systematic authentication codes. We use tight bounds for the number of rational points of these curves in estimating the probabilities of the systematic authentication codes. We compare their parameters with some existing codes in the literature. We observe that the parameters are better than the existing ones in some cases.
Citation Formats
F. Özbudak, “Constructing linear unequal error protection codes from algebraic curves,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 1523–1527, 2003, Accessed: 00, 2020. [Online]. Available: