A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even–odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...

The notion of an extremal self-dual code has been introduced in 1 . As Gleason 2 remarks onemay use invariance properties of the weight enumerator of a self-dual code to deduce upper bounds on the minimum distance. Extremal codes are self-dual codes that achieve these bounds. The most wanted extremal code is a binary self-dual doubly even code of length 72 and minimum distance 16. One frequentl...

Let $\mathcal A$ denote a set of positive integers, and let $p(\mathcal A,n)$ the associated partition function. $\beta $ be an odd integer, $P(z)$ polynomial in \mathbb F_2[z]$ order such that $P(0)=1$. J.-L

Air pollution is a big concern in a city like Delhi where more than 16 million people are exposed to severely high pollutant concentrations on an annual average basis. It is in this regard that the Government of Delhi introduced Odd-Even scheme in which plying of privately owned cars was restricted on alternate days based on the last digit (odd/even) of the registration number. However, there w...

The tweakable Even-Mansour construction generalizes the conventional Even-Mansour scheme through replacing round keys by strings derived from a master key and a tweak. Besides providing plenty of inherent variability, such a design builds a tweakable block cipher from some lower level primitive. In the present paper, we evaluate the multi-key security of TEM-1, one of the most commonly used one...

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...