Linear Codes Arise From New Complete (n,r)-arcs in PG(2,29)

Shuaa Aziz

doi:10.33899/csmj.2009.163806

Abstract

This paper presents the recently-discovered linear (n,3,d) codes over PG(2,29) that arises from a complete (n,r)-arcs which the paper(12) presented it for the first time. The aim of this paper is to formulate the recently discovered upper bounds and lower bound for (n,r)-arcs as bounds that will look familiar to coding theorists.New two lists in this paper appeared, the first list of 15 codes arranged from(164,3,156)-code up to (704,3,678)-code, the second list of 27 codes arranged from (28,3,25)-code up to (776,3,747)-code, they are appeared for the first time in this paper, all of these codes we can call them as complete codes as thier definition in this paper, they belong to the class of error-correcting codes (ECC). In this paper I made a computer programs to construct these new codes with Random Greedy Construction method (RGC) which is mentioned in (13).

Highlights

[704,3,678]-code, the second list of 27 codes arranged from [28,3,25]-code up to [776,3,747]-code, they are appeared for the first time in this paper, all of these codes we can call them as complete codes as thier definition in this paper, they belong to the class of error-correcting codes (ECC)
We saw in class how adding to the original message the parity bit or the arithmetic sum allows the detection of a error
Error-correcting codes do exactly this: they add redundancy to the original message in such a way that it is possible for the receiver to detect the error and correct it, recovering the original message

Summary

Introduction

‫[ المستنبطة‬n,3,d]-code ‫يعرض هذا البحث أحدث الشف ارت الخطية المكتشفة من النمط‬ The theory of error detecting and correcting codes (ECC) is that branch of engineering and mathematics which deals with the reliable transmission and storage of data. This paper sets new codes that are not known until now, it's codes appeared from (n,r)-arcs in the finite projective plane PG(2,29), this information in this research finds new correcting codes that were not known before, so the benefit of this paper is to use it's codes in transmitting security information among large distance without using the normal used codes that may be exposed it's security .

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Conclusion