Placement of M-Sequences over the Field Fp in the Space Rn
Ahmad Hamza Al Cheikha · International Journal of Information and Communication Sciences · 2019
Spread spectrum communication systems are widely used today in a variety of applications for different purposes such as access of same radio spectrum by multiple users (multiple access), anti-jamming capability (so that signal transmission cannot be interrupted or blocked by spurious transmission from enemy), interference rejection, secure communications, multi-path protection, etc. Several spreading codes are popular for use in practical spread spectrum systems. one of these important codes is Maximal Sequence (M-sequence) length codes, These are the longest codes that can be generated by a shift register of a specific length, The number of 1-s in the complete sequence and the number of 0-s will differ by one, Further, the auto-correlation of an m-sequence is -1, another interesting property of an M-sequence is that the sequence, when added (modulo-2) with a cyclically shifted version of itself, results in another shifted version of the original sequence. Hence, the M-sequences are also known as, pseudo-noise or PN sequences. Current article study placement M-Sequences over the finite field Fp or Mp-Sequences (where p is a prime number) in the space Rn, these sequences can be generated as a closed set under the addition. These sequences form additive groups with the corresponding null sequence that was generated by the feedback shift registers. Such Mp-Sequences see a great application in the forward links of communication channels. Furthermore, they form coders and decoders that combine the information by p during the connection process with the backward links of these channels. These sequences scrutinize the transmitted information to enable it to reach the receivers in an accurate form. This study has defined eminent surfaces in the vector space ‘R’ having dimensions of ‘n’ as quadratic forms, spheres, and planes that contain these sequences.