In DNA data storage and computation, DNA strands are required to meet certain combinatorial constraints. This paper shows how some of these constraints can be achieved simultaneously. First, we use the algebraic structure of irreducible cyclic codes over finite fields to generate cyclic DNA codes that satisfy reverse and complement properties. We show how such DNA codes can meet constant guanine-cytosine content constraint by MacWilliams-Seery algorithm. Second, we consider fulfilling the run-length constraint in parallel with the above constraints, which allows a maximum predetermined number of consecutive duplicates of the same symbol in each DNA strand. Since irreducible cyclic codes can be represented in terms of the trace function over finite field extensions, the linearity of the trace function is used to fulfill a predefined run-length constraint. Thus, we provide an algorithm for constructing cyclic DNA codes with the above properties including run-length constraint. We show numerical examples to demonstrate our algorithms generating such a set of DNA strands with all the prescribed constraints.

In this letter, we present a general construction of sequence sets with low correlation zone, which is based on finite fields and the balance property of some functions. The construction is more flexible as far as the partition of parameters is concerned. A simple example is also given to interpret the construction.

Some new generalized cyclotomic sequences defined by C. Ding and T. Helleseth are proven to exhibit a number of good randomness properties. In this paper, we determine the defining pairs of these sequences of length pm (p prime, m ≥ 2) with order two, then from which we obtain their trace representation. Thus their linear complexity can be derived using Key's method.

Based on trace function over finite field GF(pn ), new construction of generalized Hadamard matrices with order pn is presented, where p is prime and n is even. The rows in new generalized Hadamard matrices are cyclically distinct and have large linear span, which greatly improves the security of the system employing them as spreading sequences.

A new class of sextic residue sequences of period prime p=4u2+27=6f+1 ≡ 3 ( mod 8) are presented. Their trace function representations are determined. And the exact value of the linear complexity is derived from the trace function representations. The result indicates that the new sextic sequences are quite good from the linear complexity viewpoint.

In this letter, we examine the linear complexity of some 3-ary sequences, proposed by No, of period 3n-1(n=3ek, e, k integer) with the ideal autocorrelation property. The exact value of linear complexity k(6e)w is determined when the parameter r =. Furthermore, the upper bound of the linear complexity is given when the other forms of the value r is taken. Finally, a Maple program is designed to illustrate the validity of the results.