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Algorithms and Implementation for P-adic Cyclic Codes Using Exact Arithmetic Library Developed for Quantum Computing
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lu, Chao |
| Copyright Year | 2007 |
| Abstract | 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. |
| File Format | PDF HTM / HTML |
| DOI | 10.21236/ada473068 |
| Alternate Webpage(s) | https://apps.dtic.mil/dtic/tr/fulltext/u2/a473068.pdf |
| Alternate Webpage(s) | https://doi.org/10.21236/ada473068 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
