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We develop a new algorithm to compute determinants of all possible Hankel matrices made up from a given finite length sequence over a finite field. Our algorithm fits within the dynamic programming paradigm by exploiting new recursive relations on the determinants of Hankel matrices together with new observations concerning the distribution of zero determinants among the possible matrix sizes allowed by the length of the original sequence. The algorithm can be used to isolate very efficiently linear shift feedback registers hidden in strings with random prefix and random postfix for instance and, therefore, recovering the shortest generating vector. Our new mathematical identities can be used also in any other situations involving determinants of Hankel matrices. We also implement a parallel version of our algorithm. We compare our results empirically with the trivial algorithm which consists of computing determinants for each possible Hankel matrices made up from a given finite length sequence. Our new accelerated approach on a single processor is faster than the trivial algorithm on 160 processors for input sequences of length 16384 for instance.

The Castillos Lagoon has been a research focus regarding sea level fluctuations and associated climatic changes during the Holocene due to its well-preserved record of geomorphological, stratigraphic, and geoarchaeological structures. In this paper, two series of OSL (Optically Stimulated Luminescence) datings will be presented. The first one comes from a system of cheniers situated north of the Castillos Lagoon. The data obtained show that at least during a 1,200 year period, counting from a few years before 2460 yr BP, there was a process of progradation of the lagoon coast and the development of a chenier plain, consistent with a gradual drop in sea level, within a scenario of relatively stable conditions. The second series, proceeding from the first beach ridge adjacent to the lagoon coast, has allowed to determine that this stripe is current and therefore still under formation, or recently formed, permitting to obtain a direct measurement of the difference between its height and the lagoon level related to the moment of its formation that may be correlated to analogous historical records.

In this work, a series of data is presented, which is obtained by elemental analysis and edaphic analysis of the matrix of three mounds of the Garcia Ricci site, located to the south of the basin of the Merin lagoon, Uruguay. These data will contribute in increasing the knowledge of the construction processes of the mounds. The elemental composition data of the matrix indicate possible variations in the composition and origin of the materials used to elevate the mounds. The data obtained by edaphological techniques would indicate that during the construction, significant amounts of organic matter were incorporated. But the relatively low amounts of organic matter in the matrix lead us to admit that it had to be degraded. By focusing on the large amounts of burned earth that compose the Matrix, we were able to consider that part of the organic matter could have been plant fuel. This would have burned to promote the thermal alteration of the sediments that form the mounds. This paper refers to the traditional practices of soil thermal alteration to address the possible procedures and their consequences. Finally, it is pointed out that the recursive use of these practices led to the formation of patches within the landscape. Its implantation and growth for millennia were gradually modifying the landscape and particularly the distribution and circulation of plant and animal species, including humans. Pyrotechnology would have played a very important role in this modification.

In this work, constructions of ordered covering arrays are discussed and applied to obtain new upper bounds on covering codes in Rosenbloom-Tsfasman spaces (RT spaces), improving or extending some previous results.

This paper concerns an exhaustive search for normal bases with minimum complexity in finite fields \(\mathbb {F}_{2^n}\) over \(\mathbb {F}_2\) for \(n \le 46\). This is a followup paper to [11], which appeared one decade ago in 2008 and completed the cases \(n \le 39\). We extend the results in [11] by taking advantage of a combination of algorithmic improvements, more efficient implementations and massive parallelism.

We survey open problems for univariate polynomials over finite fields. We first comment in some detail on the existence and number of several classes of polynomials. The open problems in that part of the survey are of a more theoretical nature. Then, we center on classes of low-weight (irreducible) polynomials. The conjectures here are more practically oriented. Finally, we give brief descriptions of a selection of open problems from several areas including factorization of polynomials, special polynomials (APN functions, permutations), and relations between rational integers and polynomials.