General Error Locator Polynomials for Binary Cyclic Codes With <formula formulatype="inline"><tex>$t \le 2$</tex></formula> and <formula formulatype="inline"> <tex>$n < 63$</tex></formula>

Abstract

In this paper, we show that a recently proposed algorithm for decoding cyclic codes may be applied efficiently to all binary cyclic codes with tles2 and n<63. This is accomplished by providing structure theorems for the codes in this range and classifying the relevant cases