Primitive Pythagorean codes

Random Sequences from Primitive Pythagorean Triples

This paper shows that the six classes of PPTs can be put into two groups. Autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D (in which the largest term is divisible by 5) are different from the other four classes in their randomness properties if they are ordered by the largest ter...

Coding Theory Pythagorean Codes Massoud Malek

The leg c , is called the hypotenuse. If no other number except one divides both a and b, then the triangle is called “primitive Pythagorean triangle” or just “PPT”. The smallest and best-known PPT is (3, 4, 5). Ancient clay tablets from Babylonia indicate that more than 1000 years before Pythagoras, the Babylonians demonstrated an awareness of at least 15 triangles. In ancient Egypt, the (3, 4...

Indexing Properties of Primitive Pythagorean Triples for Cryptography Applications

This paper presents new properties of Primitive Pythagorean Triples (PPT) that have relevance in applications where events of different probability need to be generated and in cryptography.

Binary Cyclic codes with two primitive nonzeros

In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of Tr(x) over F2m in the case wherem = 2t, d = 3+2 t+1 and gcd(d, 2−1) = 1.

On Commutation and Primitive Roots of Codes