Applications of quasi-uniform codes to storage

Abstract

We consider the design of quasi-uniform codes from dihedral 2-groups. Quasi-uniform codes have the distinctive feature of allowing codeword coefficients to live in different alphabets. We obtain a bound on the minimum distance of quasiuniform codes coming from p-groups as a function of the number of p-ary codeword components. We study possible applications of such codes to storage, where the minimum distance is important to allow object retrieval, yet binary coefficients are preferred for fast computations, for example during repairs.

Quasi-uniform codes and information inequalities using group theory

“…Some bounds satis ied by the these codes are also computed there. Finally in Chapter 8, some applications of quasi-uniform codes in storage (published in [40]) are proposed with the help of abelian representability.…”

“…Suppose a data object (u 1 , u 2 , u 3 ) needs to be stored. Consider the following storage allocation [40]: We easily notice that three failures at most can be tolerated (corresponding to a minimum distance of 4 indeed): u 2 is present only in nodes 2,3,4 and 5, so if these four nodes fail, u 2…”