On the shape of the general error locator polynomial for cyclic codes

الأصل · EN

A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along with several results for infinite classes of cyclic codes with t=2 and t=3. From these, a theoretically justification of the sparsity of the general error locator polynomial is obtained for all cyclic codes with t≤ 3 and n<63, except for three cases where the sparsity is proved by a computer check. Moreover, we discuss some consequences of our results to the understanding of the complexity of bounded-distance decoding of cyclic codes.