The code C is the set of vectors satisfying XH =O. In many information betwen [ and n. Using a slight modification of a applications it is desirable to know, for a given weight w, technique of Lipster [7], we obtain whether C contains any words of weight w, i.e., whether there is a vector of weight w satisfying XH = 0. Again, the best general algorithm known for deciding this requires an exponential search, in this case through all 2k codewords, and a faster algorithm would be highly desirable.

No abstract

No abstract

No abstract

No abstract

Abstract.This paper reviews some of the known algorithms for factoring polynomials over finite fields and presents a new deterministic procedure for reducing the problem of factoring an arbitrary polynomial over the Galois field GF(p"!) to the problem of finding the roots in GF(p) of certain other polynomials over GF(p). The amount of computation and the storage space required by these algorithms are algebraic in both the degree of the polynomial to be factored and the logarithm of the order of the finite field.Certain observations on the application of these methods to the factorization of polynomials over the rational integers are also included.

We present here an algorithm for factoring a given polynomial over GF(q) into powers of irreducible polynomials. The method reduces the factorization of a polynomial of degree m over GF (q) to the solution of about m(q — 1)/q linear equations in as many unknowns over GF(q).

No abstract