On the Error-Correcting Performance of some Binary and Ternary Linear Codes

In this work, we determine the coset weight spectra of all binary cyclic codes of lengths up to 33, ternary cyclic and negacyclic codes of lengths up to 20 and of some binary linear codes of lengths up to 33 which are distance-optimal, by using some of the algebraic properties of the codes and a computer assisted search. Having these weight spectra the monotony of the function of the undetected error probability after t-error correction P(t)ue (C,p) could be checked with any precision for a linear time. We have used a programm written in Maple to check the monotony of P(t)ue (C,p) for the investigated codes for a finite set of points of p € [0, p/(q-1)] and in this way to determine which of them are not proper.

Simulation-based Approach to Verification of Logical Descriptions with Functional Indeterminacy

A verification task of proving the equivalence of two descriptions of the same device is examined for the case, when one of the descriptions is partially defined. In this case, the verification task is reduced to checking out whether logical descriptions are equivalent on the domain of the incompletely defined one. Simulation-based approach to solving this task for different vector forms of description representations is proposed. Fast Boolean computations over Boolean and ternary vectors having big sizes underlie the offered methods.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Reasoning Methods for Designing and Surveying Relationships Described by Sets of Functional Constraints

This work is supported by the Hungarian Scientific Research Fund (OTKA), grant T042706.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

Necessary and Sufficient Conditions for the Extendability of Ternary Linear Codes

We give the necessary and sufficient conditions for the extendability of ternary linear codes of dimension k ≥ 5 with minimum distance d ≡ 1 or 2 (mod 3) from a geometrical point of view.

New Binary Extremal Self-Dual Codes of Lengths 50 and 52

* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995.

New Binary $[70,35,12]$ Self-Dual and Binary $[72,36,12]$ Self-Dual Doubly-Even Codes

∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99

Sensitivity and Bias within the Binary Signal Detection Theory, BSDT

Similar to classic Signal Detection Theory (SDT), recent optimal Binary Signal Detection Theory (BSDT) and based on it Neural Network Assembly Memory Model (NNAMM) can successfully reproduce Receiver Operating Characteristic (ROC) curves although BSDT/NNAMM parameters (intensity of cue and neuron threshold) and classic SDT parameters (perception distance and response bias) are essentially different. In present work BSDT/NNAMM optimal likelihood and posterior probabilities are analytically analyzed and used to generate ROCs and modified (posterior) mROCs, optimal overall likelihood and posterior. It is shown that for the description of basic discrimination experiments in psychophysics within the BSDT a ‘neural space’ can be introduced where sensory stimuli as neural codes are represented and decision processes are defined, the BSDT’s isobias curves can simultaneously be interpreted as universal psychometric functions satisfying the Neyman-Pearson objective, the just noticeable difference (jnd) can be defined and interpreted as an atom of experience, and near-neutral values of biases are observers’ natural choice. The uniformity or no-priming hypotheses, concerning the ‘in-mind’ distribution of false-alarm probabilities during ROC or overall probability estimations, is introduced. The BSDT’s and classic SDT’s sensitivity, bias, their ROC and decision spaces are compared.

On some Properties of Boolean Functions and Their Binary Decision Diagrams

Иво Й. Дамянов - Манипулирането на булеви функции е основнo за теоретичната информатика, в това число логическата оптимизация, валидирането и синтеза на схеми. В тази статия се разглеждат някои първоначални резултати относно връзката между граф-базираното представяне на булевите функции и свойствата на техните променливи.