Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

Poset and block metrics were introduced in recent years as alternative metrics to study error
correcting codes. Poset-block codes were introduced in 2008, encompassing both poset …

In 1995, Brualdi et al.[14] introduced the concept of a metric on a vector space determined
by a partial order over a finite set, a poset. These are the so-called poset metrics, that …

Let P=([n],≤ P) be a poset on [n]={1, 2,⋯, n}, F qn be the linear space of n-tuples over a finite
field Fq and w be a weight on F q. In this paper we consider metrics on F qn which are …

In this work we present a canonical-systematic form of a generator matrix for linear codes
whith respect to a hierarchical poset metric on the linear space Fn q. We show that up to a …

We study a new family of metrics, weighted poset block metric, which generalizes the
weighted coordinates poset metric introduced by Panek and Pinheiro (IEEE Trans Inf Theory …

In this paper, we introduce codes equipped with pomset block metric. A Singleton type
bound for pomset block codes is obtained. Code achieving the Singleton bound, called a …

Let H be the cartesian product of a family of abelian groups indexed by a nonempty finite set
Ω. A given poset P=(Ω,≼ P) and a map ω: Ω→ ℝ+ give rise to the (P, ω)-weight on H, which …

In this paper, we prove that a poset-block space admits a MacWilliams-type identity if and
only if the poset is hierarchical, and at any level of the poset, all the blocks have the same …

We obtain the Singleton bound for poset block codes and define a maximum distance
separable poset block code (MDS (P, π)-code) as a code meeting this bound. We extend the …