Lexicographic codes: Error-correcting codes from game theory
IEEE Transactions on Information Theory
Enumerative combinatorics
On Perfect Codes and Related Concepts
Designs, Codes and Cryptography
Johnson type bounds on constant dimension codes
Designs, Codes and Cryptography
Recursive code construction for random networks
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A Random Linear Network Coding Approach to Multicast
IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
A Rank-Metric Approach to Error Control in Random Network Coding
IEEE Transactions on Information Theory
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Packing and covering properties of subspace codes for error control in random linear network coding
IEEE Transactions on Information Theory
Constant-rank codes and their connection to constant-dimension codes
IEEE Transactions on Information Theory
Recursive code construction for random networks
IEEE Transactions on Information Theory
A complete characterization of irreducible cyclic orbit codes and their Plücker embedding
Designs, Codes and Cryptography
Rank subcodes in multicomponent network coding
Problems of Information Transmission
Hi-index | 755.02 |
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can playa key role for solving coding problems in the projective space. In this paper, We propose a method to design error-correcting codes in the projective space. We use a multilevel approach to design our codes. First, we select a constant-weight code. Each codeword defines a skeleton of a basis for a subspace in reduced row echelon form. This skeleton contains a Ferrers diagram on which we design a rank-metric code. Each such rank-metric code is lifted to a constant-dimension code. The union of these code is our final constant-dimension code. In particular, the codes constructed recently by Koetter and Kschischang are a subset of our codes. The rank-metric codes used for this construction form a new class of rank-metric codes. We present a decoding algorithm to the constructed codes in the projective space. The efficiency of the decoding depends on the efficiency of the decoding for the constant-weight codes and the rank-metric codes. Finally, we use puncturing on our final constant-dimension codes to obtain large codes in the projective space which are not constant-dimension.