DECODING OF ORBIT CODES

Abstract

Subspace codes have gained considerable attention during the last decade due to their crucial role in random network coding. Subspace codes are defined as sets of vector spaces over a finite field. Subspace codes can be used to correct errors and erasures in network with linear network coding. Networks are exposed to noise such that messages can be lost or modified during the transmission of subspace V. Therefore some vectors of V might be lost and we will received smaller subspace V 0 < V. On the other hand, vectors which are not contained in V might be received. These erroneous vectors span a vector space E, thus R = V 0 ⊕ E will be received. In fact, there are two types of errors that may occur during transmission, a decrease in dimension, which is called an erasure and an increase in dimension, called an insertion

Keywords

• Subspace codes,Constant dimension subspace codes,Grassmannian,Group action,Orbit codes.

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