| Conflict-avoiding codes(CACs) have been used in multiple-access collision channel without feedback. The number of codewords is the number of potential users that can be supported in the system. A CAC with maximal code size is said to be optimal. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. It is useful to construct optimal CACs. Pseudo-random sequences are widely used in spread spectrum communication systems, code division multiple access systems, global positioning systems,and stream ciphers etc. In these applications, especially for pseudo-random sequences with good properties have strong demand.The autocorrelation and linear complexity are two important properties of pseudo-random sequence. This dissertation mainly investigates the construction of optimal conflict-avoiding codes, autocorrelation and cross-correlation values of binary generalized cyclotomic sequences with length pq, linear complexity of polynomial sequences and the trace representation of polynomial quotient sequences.The main results are shown as follows:1. First of all, we introduce a new construction of optimal equi-difference CACs and therefore we obtain the maximal size of equi-difference CACs for any odd prime length.This result is superior to the known ones as. We also give a hypothesis to construct optimal tight code C ∈ CAC(L, 3) of any odd prime length L. Through constructing the optimal CACs, we obtain the maximal size of CACs of odd prime length L and weight 3. This size is better than the known upper bound. We also show the number of equi-difference codewords and the number of non equi-difference codewords in a tight CAC. So, in this method we can construct tight optimal non equi-difference CACs which is different from the codes known construction. Secondly, by giving a new modified recursive construction, we obtain a construction of an optimal tight CAC for any odd length L and weight 3. Non equidifference optimal CACs can also be constructed in this way. So this recursive construction is different from the ones. Finally, we present a conjecture and check it in computer. The result shows that this conjecture is always right.2. Several kinds of Whiteman’s generalized cyclotomic sequence of order 6 are constructed. Their autocorrelation and cross-correlation values are determined using the knowledge of cyclotomic numbers, finite field and number theory,etc. The autocorrelation values are in{-1, 3,-5, pq} and the cross-correlation values are linear relationship to the period pq if the parameters are chosen carefully.3. Several kinds of polynomial quotient sequences of length p2 are constructed based on the polynomial quotient module p. The linear complexity and minimal polynomial are also determined by the factoring of polynomials theory and the roots of its characteristic polynomial, respectively. The linear complexity can take the values {p2-1, p2-p, p2-p+1},or {p2- 1, p2- p}. The result shows that its linear complexity is larger than half of its period. By B-M algorithm, the sequence is considered to be good from the viewpoint of linear complexity.4. It is well known that every sequence can be represented using trace function(trace representation). Trace representations of sequences can help us to analyze the sequences’ pseudo-random properties, such as autocorrelation values, linear complexity,etc. We first present the trace representations of some polynomial quotients, and also verify the correctness of the linear complexity presented before.
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