ISSN: 2250-3005 - ijcer

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 83. The power M of the assembly S,S ,..., bounded below by the expression:S is defined by the number of non-zero orbits of the code V and is1 2 SM2 1M . (3)nThe equality holds in case of the maximum period of the sequence of all the orbits forming the code, i.e. if the code is V a setof orbits, formed by sequences of maximum length (m-sequences).Let’s consider the most general case where the binary group , k, dGF 2 is given by checking polynomial of:k n code under m 1s1sss i12i22 iu2x f x f x ... f x x x ... x h i1i2i, (4)u iwhere, fi 1x, fi 2x, ..., fi ux– u arbitrary row of the following minimal polynomial elements 1 mGF2i 2 m i GF2, ..., u m1 GF2 respectively, where the order of the elements i 2, i iu, ...,mmultiplicative group of a finite field GF 2, n 2m m 1, – a primitive element of the finite field GF 2, n 2m 1. , is equal to the order of theLet’s consider, without loss of generality that i 1 1. Let’s define the check and generator polynomial as follows:ss i22 iu2x ... x m1s 2h x x, s0nxm jsj2 x x 1g x .hj1,i,..., i2Schematically, the process of forming of the check and generator polynomial is shown in Fig. 2. The symbol v stands for themnumber of the classes of conjugate elements that make up a mult iplicative group of a finite field GF 2(elements1 ,classes (elementscorresponding2 , ...,j ,2m1 2 j , ...,m12us0. The first class) contains m conjugacy (which determines the primitive element ). The followingj2 m 2 ) contain jm conjugacy (m j is defined as the smallest positive integer for which the equality:mj2j mmod21j .If the order of the multiplicative group of a prime number, that is, when:2 m 1 prime number ,then: j:m m .A single element of the field 0 1forms an additional conjugate class of one element.Fig. 3 shows the corresponding distribution of the elements of a finite field in the polynomialsfinite field of the first u conjugate classes are the roots of the check polynomialwhich holds the roots of the check polynomialz (z) mod(2m 1), is done, that is:z maxs0,...,m1j m divides evenly m ) j 1..v. For each j 1..vjh xand g x. Elements of ah x. A range of elements of a finite field,h x, is determined by the largest value z , for which the conditions ms ms m mod21, i2 mod21, ..., i2 mod21}{ 22u.||Issn 2250-3005(online)|| ||December||2012|| Page 239