Results 21 to 25 of about 1,066,179 (25)

Full Characterization of Minimal Linear Codes as Cutting Blocking Sets [PDF]

arXiv, 2019
In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking sets. As a direct result, minimal projective codes of dimension $3$ and $t$-fold blocking sets with $t\ge 2$ in ...
arxiv  

Information sets from defining sets in abelian codes [PDF]

arXiv, 2011
We describe a technique to construct a set of check positions (and hence an information set) for every abelian code solely in terms of its defining set. This generalizes that given by Imai in \cite{Imai} in the case of binary TDC codes.
arxiv  

Two-dimensional Constacyclic Codes over $\mathbb{F}_q$ [PDF]

arXiv
We consider two-dimensional $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_{q}$ of area $M N$, where $q$ is some power of prime $p$ with $\gcd(M,p)=1$ and $\gcd(N,p)=1$. With the help of common zero (CZ) set, we characterize 2-D constacyclic codes.
arxiv  

Set Transformation: Trade-off Between Repair Bandwidth and Sub-packetization [PDF]

arXiv
Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization level being one, however, they require large repair bandwidth defined as the total amount of symbols downloaded ...
arxiv  

Stopping Set Analysis for Concatenated Polar Code Architectures [PDF]

arXiv
This paper investigates properties of concatenated polar codes and their potential applications. We start with reviewing previous work on stopping set analysis for conventional polar codes, which we extend in this paper to concatenated architectures.
arxiv