This contribution describes new GF (p) multipliers, for p > 2, specially suited for GF (p) multiplication. We construct truth tables whose inputs are the bits of the multiplicand and multiplier and whose output are the bits that represent the modular product. However, contrary to previous approaches, we don’t represent the elements of GF (p) in the normal binary positional system. Rather, we ch...

It is demonstrated how classes of linear (n, k)-codes can be enumerated using cycle index polynomials and other methods from algebraic combinatorics. Some results of joined work [9] with Prof. Kerber from the University of Bayreuth on the enumeration of linear codes over GF (q) are presented. Furthermore I will give an introduction to enumeration under finite group actions. At first let me draw...

An information reconciliation method for continuous-variable quantum key distribution with Gaussian modulation that is based on non-binary low-density paritycheck (LDPC) codes is presented. Sets of regular and irregular LDPC codes with different code rates over the Galois fields GF(8), GF(16), GF(32), and GF(64) have been constructed. We have performed simulations to analyze the efficiency and ...

In this paper, we discuss some methods of constructing frequency/time hopping (FH/TH) sequences over GF (p) by taking successive k-tuples of given sequences over GF (p). We are able to characterize those p-ary sequences whose k-tuple versions now over GF (p) have the maximum possible linear complexities (LCs). Next, we consider the FH/TH sequence generators composed of a combinatorial function ...

For an odd prime p and each non-empty subset S ⊂ GF (p), consider the hyperelliptic curve XS defined by y = fS(x), where fS(x) = Q a∈S(x− a). Using a connection between binary quadratic residue codes and hyperelliptic curves over GF (p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S...

We propose a method for rapid development of dialogue systems where a Grammatical Framework (GF) grammar is compiled into a complete VoiceXML application. This makes dialogue systems easy to develop, maintain, localize, and port to other platforms, and can improve the linguistic quality of generated system output. We have developed compilers which produce VoiceXML dialogue managers and ECMAScri...

_.a conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite fieM, GF(qg ). A pipeline structure is used to implement this prime factor DFT over GF(qn). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode ReedSolomon codes. Such a pipeline fast prime factor DFT algorithm over G...

This contribution describes a new class of arithmetic architectures for Galois fields GF (2k). The main applications of the architecture are public-key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF (2k) as GF ((2n)m), where k = n · m. The approach explores bit parallel arithmetic in the subfield GF (2n), and...

A new class of pseudo-random sequences (called cascaded GMW-type permutation polynomial (CGPP) sequences) over GF (qn) is constructed using a system of n orthogonal cascaded GMW functions in GF (q). Their statistical properties are given. Classification, evaluation, and implementation of the CGPP sequences are derived. A sequence generated by mapping elements of a CGPP sequence into GF (q) is a...