On the Probability of Undetected Error for Over-Extended Reed-Solomon Codes

We derive upper and lower bounds on the weight distribution of Over-Extended Reed-Solomon (OERS) codes. Using these bounds, we obtain tight upper and lower bounds on the probability of undetected error for OERS codes on q-ary symmetric channels.

I. Introduction

In some applications, error correcting codes have been used as pure error detection codes. In particular, Reed-Solomon (RS) codes have been used for error detection in some disk drives since the 1990's because they have excellent error detection capabilities and do not exhibit the undesirable behavior characteristic of certain shortened binary cyclic redundancy check (CRC) codes [1]. A further example is the USB interface standard [2], which specifies the use of a Hamming code for error detection.