Abstract
Walsh Sequences and M-Sequences used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in correct form, specially in the pilot channels, the Sync channels, and the Traffic channel.
 This research is useful to generate new sets of sequences (which are also with the corresponding null sequence additive groups) by compose Walsh Sequences and
 M-sequences with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication.
Highlights
Walsh sequences of order 2k, which are generated by the binary representation of Walsh functions of order N = 2k, form a group under 2 addition
First: We suppose a1 is a non zero M-Sequence generated by the non homogeneous linear recurring sequence (1) of order m with the prime characteristic polynomial: f (x) xm m 1xm 1 ... 1x 0
Second: We suppose W2*n wi, i 1,2,...,2n 1 the set of all Walsh sequences of order 2n except the null sequence w0 each of these wi contains 2 n 1 of “1”s and the same number of “0” and W2*n is closed under the addition
Summary
In 1923, J.L. Walsh defined a system of orthogonal functions that is complete over the normalized interval (0,1). Walsh sequences of order 2k , which are generated by the binary representation of Walsh functions of order N = 2k , form a group under 2 addition (addition group). The set of these sequences except W0 forms orthogonal closed set and the number of “1”s is equal the number of “0” and each of them is equal 2 k 1 . The Walsh functions can be generated by any of the following methods: 1. 3. Exploiting the symmetry properties of Walsh functions.
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