The Constructions Of Orbit Subspace Codes

Information transmission and sharing are the most important purpose of the net-work.In traditional network,data are transmitted through intermediate nodes by the way of storing and forwarding,which have inherent disadvantages of the simple s-tore and forward mechanism.The intermediate node was required to transmit data through "storing-coding-forwarding" in the network coding and the receiver recover the original data by decoding the received data.It has been proved theoretically,linear network coding can maximize network throughput capacity,and has excellent stability and adaptability.Because each intermediate node selects coefficients randomly to mix the received information linearly,and then transmit to the next node.This feature makes it easy to get contaminated attack and entropy attack.To overcome this shortcoming,Kotter and Kschischang describe random network coding through algebraic method in 2008.Each packet is one of the vector in Fqn,the linear combination of these pack-ets forms the linear subspace of Fqn.Therefore,a linearized subspace is considered as a codeword,the set of some subspaces form a subspace code.In the network cod-ing,transmission of information is equivalent to the transmission of a subspace.The distance between two codewords is defined by the codimension of the corresponding subspace.Later,subspace codes are widely concerned and studied.In this paper,we mainly study the construction and parameter analysis of some subspace codes,mainly including:(1)A class of constant dimension cyclic orbit code similar to partial spread subspace codes is constructed.The cardinality of the code is qn-1/q-1,1he minimum distance is 4,the dimension of each code is 3.(2)Two classes of orbit subspace codes with very dimension are constructed by means of linearized polynomials,that is,the codewords in subspace codes have two dimensions.The car-dinality of the constructed subspace codes is larger than that of the constant dimension subspace codes,and the minimum distance is close to the constant dimension subspace codes.(3)The kernel of linearized polynomials are acted by Frobenius transformation.A kind of very dimension subspace code is constructed,whose cardinality is much larg-er than the constant dimension subspace codes,but the minimum distance is close to the constant dimension subspace codes.