Linear codes arise from new complete (n, r)‎-arcs in PG (2, 29)‎

Abstract EN

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].