An improvement on the bounds of Weil exponential sums over Gallois rings with some applications

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 distance of certain trace codes over Z(p)2 and the bounds on the correlation of certain nonlinear p-ary sequences.


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...
The Sphere Packing Bound via Augustin's Method
Nakiboğlu, Barış (Institute of Electrical and Electronics Engineers (IEEE), 2019-02-01)
A sphere packing bound (SPB) with a prefactor that is polynomial in the block length n is established for codes on a length n product channel W-[1,W- n], assuming that the maximum order 1/2 Renyi capacity among the component channels, i.e. max(t is an element of[1, n]) C-1/2, W-t, is O(ln n). The reliability function of the discrete stationary product channels with feedback is bounded from above by the sphere packing exponent. Both results are proved by first establishing a non-asymptotic SPB. The latter re...
Constructing linear unequal error protection codes from algebraic curves
Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2003-06-01)
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.
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...
Sampling of the Wiener Process for Remote Estimation Over a Channel With Random Delay
Sun, Yin; Polyanskiy, Yury; Uysal, Elif (Institute of Electrical and Electronics Engineers (IEEE), 2020-02-01)
In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator over a channel that is modeled as a queue. The estimator reconstructs an estimate of the real-time signal value from causally received samples. We study the optimal online sampling strategy that minimizes the mean square estimation error subject to a sampling rate constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determ...
Citation Formats
S. Ling and F. Özbudak, “An improvement on the bounds of Weil exponential sums over Gallois rings with some applications,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 2529–2539, 2004, Accessed: 00, 2020. [Online]. Available: