| The cellular technology plays an important role in the Code Division Multiple Access(CDMA)system.One of the basic requirements is that the system can provide enough orthogonal sequences which can serve more users.To avoid the interference arising from the re-use of a codeword in a close cell,the system must guarantee the correlation of the codewords assigned to adjacent cells is 0,while the correlation of codewords assigned to non-adjacent cells is as small as possible.Based on the existing method of constructions of orthogonal sequence sets and their cell assignment,the author obtains the main results as follows.(1)Different semi-bent functions are used to construct the sets of orthogonal sequences and their cell assignment.Firstly,based on the properties of multi-dimension semi-bent function,a cellular system with the code length of 2~5 can be presented directly.Secondly,the number of variables of this semi-bent function increases by using direct sum construction.Then a regular tessellation of hexagonal cells with the length of 2~n(n ≥3,n ≠5,odd)and re-use distance of D4= is obtained.At last,the situation extends to be even(n≥6).It is found that the capacity of orthogonal sequence sets constructed by this function reaches to 22n-and the re-use distance of the corresponding cellular arrangement meets the requirement of D ≥4,which is the same as the best result known.In the aspect of the range of the semi-bent function used when constructing the orthogonal sequence sets,the number of the semi-bent functions is larger than that in the existing method.In response to potential communication security,this semi-bent function can use a mapping without a non zero linear structure(when n ≥5),which is more secure than using a linear function in the face of potential potential danger.(2)A new construction of multi-output plateaued functions is given and this kind of functions is used to construct the sets of orthogonal sequencesFirstly,a new construction of plateaued(semi-bent)functions is given.Based on this,a semi-bent function with more variables is given by using direct sum construction and corresponding orthogonal sequence sets and cellular assignment are obtained.Secondly,by modifying this function and bent concatenation,a semi-bent function with even variables is given.Based on this,the orthogonal sequence sets and cellular assignment are constructed.It is showed that the orthogonal sequence sets and cellular assignment generated by the function constructed using this new method has the same result of the re-use distance and capacity.In terms of communication security,this semi-bent function can use a mapping without a non zero linear structure(when n ≥5),which is more secure than using a linear function in the face of potential potential danger. |
