A general algorithm to design sets of all possible one dimensional unipolar orthogonal codes of same code length and weight

This paper describe a general scheme to design all the uni-polar codes characterized by parameter (n, w). The binary sequence of length `n´ (`n´ bits) and weight `w´ (number of bit `1´s in the sequence) with its n-1 circular shifted versions represent the same code. These codes can be further put in different subsets characterized by (n, w, λ_a, λ_c), where λ_a and λ_c are auto-correlation and cross-correlation constraint respectively. All the codes within a set are called orthogonal to each other. In reality, they are pseudo orthogonal as cross-correlation is non-zero. With parameter (n, w, λ_a, λ_c), there can be many sets each containing a number of orthogonal codes. All the codes in one set are always orthogonal to each other but not necessarily orthogonal to the codes in other sets. The code design scheme presented in this paper, can design all possible sets of codes. Users can select the code set as per their requirements. These uni-polar one dimensional orthogonal codes have their application in incoherent optical code division multiple access systems. The uni-polar optical orthogonal code can be generated by putting a single optical pulse at every position of bit `1´ and no pulses at the positions of bit `0´s in the sequence.