Algorithms and Implementation for P-adic Cyclic Codes Using Exact Arithmetic Library Developed for Quantum Computing
Abstract
The first part of the research is that we have expanded the Exact Scientific Computational Library (ESCL), and Dixon's algorithm on rational N by N matrix inverse was implemented. We studied and experimented the relation of required length M of p-adic expansion and the prime p, and the possible use of the length of periodicity of a rational number's p-adic expansion in determining the length of required M in rational matrix operations. The second part of the work is to develop and implement computational algorithms for p-adic cyclic code generation, which is based on the results of the paper, "Modular and p-adic cyclic codes", by A.R. Calderbank and N.J.A. Sloane. Algorithms and software have been developed to give an alternative solution to factorize the polynomial X"-1 over the ring of integers modulo p(a), where p is a prime not dividing n, and it can generate the table of cyclic codes using the divisors of X"-1 as their generator polynomials. All the implementation of ESCL is in C++, as well as the software to generate p-adic cyclic codes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 16, 2007
- Accession Number
- ADA473068
Entities
People
- Chao Lu
Organizations
- Towson University