Generalization of the lee weight to Ζpᵏ

We introduce a new extension of the Lee weight to Ζpᵏ and later to Galois rings GR(pᵏ,m). The weight we define is a non-homogeneous weight and is different than the one that is generally labeled as "generalized Lee weight". Unlike the case of generalized Lee weight, we define a distance-preserving Gray map from (Ζpᵏ, extended Lee distance)to (Fppᵏ⁻¹, Hamming distance), thus making our extension practical for coding theory purposes.Publisher's Versio

On the Properties of Error Patterns in the ConstantLee Weight Channel

The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar. This problem is of particular interest for cryptographic applications, like for example Lee metric code-based cryptosystems, since an attacker may use scalar multiplication to reduce the Lee weight of the error vector and thus to reduce the complexity of the corresponding generic decoder. The scalar multiplication problem is analyzed in the asymptotic regime. Furthermore, the construction of a vector with constant Lee weight using integer partitions is analyzed and an efficient method for drawing vectors of constant Lee weight uniformly at random from the set of all such vectors is given