A Fast Method to Estimate Partial Weights Enumerators by Hash Techniques and Automorphism Group
Journal Title: International Journal of Advanced Computer Science & Applications - Year 2017, Vol 8, Issue 9
Abstract
BCH codes have high error correcting capability which allows classing them as good cyclic error correcting codes. This important characteristic is very useful in communication and data storage systems. Actually after almost 60 years passed from their discovery, their weights enumerators and therefore their analytical performances are known only for the lengths less than or equal to 127 and only for some codes of length as 255. The Partial Weights Enumerator (PWE) algorithm permits to obtain a partial weights enumerators for linear codes, it is based on the Multiple Impulse Method combined with a Monte Carlo Method; its main inconveniece is the relatively long run time. In this paper we present an improvement of PWE by integration of Hash techniques and a part of Automorphism Group (PWEHA) to accelerate it. The chosen approach applies to two levels. The first is to expand the sample which contains codewords of the same weight from a given codeword, this is done by adding a part of the Automorphism Group. The second level is to simplify the search in the sample by the use of hash techniques. PWEHA has allowed us to considerably reduce the run time of the PWE algorithm, for example that of PWEHA is reduced at more than 3900% for the BCH (127,71,19) code. This method is validated and it is used to approximate a partial weights enumerators of some BCH codes of unknown weights enumerators.
Authors and Affiliations
Moulay Seddiq EL KASMI ALAOUI, Saïd NOUH, Abdelaziz MARZAK
Unsupervised Morphological Relatedness
Assessment of the similarities between texts has been studied for decades from different perspectives and for several purposes. One interesting perspective is the morphology. This article reports the results on a study o...
A Survey of Automated Text Simplification
Text simplification modifies syntax and lexicon to improve the understandability of language for an end user. This survey identifies and classifies simplification research within the period 1998-2013. Simplificatio...
A Secured Interoperable Data Exchange Model
Interoperability enables peer systems to communicate with each other and use the functionality of peer systems effectively. It improves ability for different systems to exchange information between cooperative systems. I...
FHC-NCTSR: Node Centric Trust Based secure Hybrid Routing Protocol for Ad Hoc Networks
To effectively support communication in such a dynamic networking environment as the ad hoc networks, the routing mechanisms should adapt to secure and trusted route discovery and service quality in data transmissi...
NHCA: Developing New Hybrid Cryptography Algorithm for Cloud Computing Environment
The amount of transmitted data through the internet become larger and larger every day. The need of an encryption algorithm that guarantee transmitting data speedily and in a secure manner become a must. The aim of the r...