General error locator polynomials were introduced in 2005 as an alternative decoding for cyclic codes. We now present a conjecture on their sparsity, which would imply polynomial-time decoding for all cyclic codes. A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along with several results for specific code families, providing evidence to our conjecture. From these, a theoretical justification of the sparsity of general error locator polynomials is obtained for all binary cyclic codes with t ≤ 2 and n <; 105, as well as for t = 3 and n <; 63, except for some cases where the conjectured sparsity is proved by a computer check. Moreover, we summarize all related results, previously published, and we show how they provide further evidence to our conjecture. Finally, we discuss the link between our conjecture and the complexity of bounded-distance decoding of the cyclic codes.

Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily optimal codes. In this paper, we identify code parameters (q, d, k), namely, field size, minimum distance, and combinatorial dimension, for which the Griesmer bound also holds in the (systematic) nonlinear case. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by explicit construction of a family of optimal systematic binary codes. On the other hand, we are able to provide some versions of the Griesmer bound holding for all the systematic codes.

We present some upper bounds on the size of nonlinear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g., the Griesmer bound, the Johnson bound, the Plotkin bound, and of linear programming bounds. One of the new bound is actually an improvement of a bound by Zinoviev, Litsyn, and Laihonen. Our experiments show that in the linear case our bounds provide the best value in a wide range, compared with all other closed-formula upper bounds. In the nonlinear case, we also compare our bound with the linear programming bound and with some improvements on it, show that there are cases where we beat these bounds. In particular, we obtain a new bound in Brouwer's table for A3(16,3).

In this paper, we show that a recently proposed algorithm for decoding cyclic codes may be applied efficiently to all binary cyclic codes with tles2 and n<63. This is accomplished by providing structure theorems for the codes in this range and classifying the relevant cases

In this work, we propose an adaptive technique for interference mitigation based on minimum variance distortionless response (MVDR) beamforming for the uplink of a WiMAX-compliant system. This method is designed to cope with time-varying interference due to the asynchronous access of users in the neighboring cells. Channel parameters needed for beamforming are obtained by exploiting both the preambles in the transmitted frames and the pilot subcarriers embedded in each information-bearing OFDM symbol. The effectiveness of the proposed technique is shown through numerical simulations of a standard WiMAX uplink over standard multipath channels

A new lower bound for the distance of cyclic codes is proposed. This bound depends on the defining set of the code, like several other bounds. The proposed bound improves upon the Bose–Chaudhuri–Hocquehghen (BCH) bound and, for some codes, improves upon the Hartmann–Tzeng bound and the Roos bound as well.

To estimate the weight distribution of a binary linear code, a linear programming approach has been proposed, which leads to the best known values for BCH (255,k). Following that approach, we propose three methods which give tighter estimates. At the same time, we find the distance of the dual of BCH [255,199,15].