Finite Higher Spin Transformations from Exponentiation

Fast exponentiation via prime finite field isomorphism

lard and Schnorr algorithm. Farther factorization of prime quadratic integer π = ρρ in the ring 4 [ 2] ±  can be done similarly. Finite field r is represented as quotient ring 4 [ 2] /( ) ± ρ  . Integer exponent k is reduced in corresponding quotient ring by minimization of absolute value of its norm. Algorithms can be used for fast exponentiation in arbitrary cyclic group if its order can b...

Algorithms for Exponentiation in Finite Fields

and infinitely many integers n, multiplication in a normal basis of Fqn over Fq can be computed with O(n logn loglogn), division with O(n log n loglogn) operations in Fq , and exponentiation of an arbitrary element in Fqn with O(n2 loglogn) operations in Fq . We also prove that using a polynomial basis exponentiation in F2n can be done with the same number of operations in F2 for all n. The pre...

Exponentiation Using Addition Chains for Finite Fields

Operads of higher transformations for globular sets and for higher magmas

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

Higher Order Context Transformations

The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive symbols of the input message. These transformations were intended to be used as a preprocessor for zero-order entropy coding algorithms like Arithmetic or H...