Linear codes from vectorial Boolean functions in the context of algebraic attacks

International audienceIn this paper, we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and certain [Formula: see text]-ary cyclic codes (which we show that they are LCD codes). We also present some properties of those cyclic codes as well as their weight enumerator. In addition, we generalize the so-called algebraic complement and study its properties

Cyclic dna codes over the ring z4 + uz4 + u2 z4

In this work, we have investigated the one generator cyclic DNA codes with reverse and reverse complement constraints over the ring R = ℤ4 +uℤ4 +u2 ℤ4 with u3 = 0. Skew cyclic codes with reverse complement constraint are constructed over R. We have also determined a one-to-one correspondence between the elements of the ring R and DNA codons satisfying the Watson-Crick complement. Finally, we have established some examples which satisfy the given constraints