Abstract

In this presentation, we give necessary and sufficient conditions (lower and upper bounds) for the existence of linear codes capable of identifying the portion of the codeword which is corrupted by errors named as key errors. An example of such a code is provided. Comparisons among the number of parity check digits of linear codes detecting/locating/correcting key errors are provided. A result on minimum weight of key errors in Hamming sense is also included in the paper.

Keywords: Parity check matrix; syndrome; standard array; hamming weight; error locating codes.

MSC: 94B05, 94B65

Pages:  43$-$54     

Volume  73 ,  Issue  1 ,  2021