How to Mask the Structure of Codes for a Cryptographic Use
Designs, Codes and Cryptography
On Cauchy matrices for remainder decoding of Reed-Solomon codes
IEEE Communications Letters
Network coding-based reliable multicast in wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Special sequences as subcodes of reed-solomon codes
Problems of Information Transmission
Block-level packet recovery with network coding for wireless reliable multicast
Computer Networks: The International Journal of Computer and Telecommunications Networking
Regenerating codes: a system perspective
ACM SIGOPS Operating Systems Review
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It is shown that the family ofq-ary generalized Reed-Solomon codes is identical to the family ofq-ary linear codes generated by matrices of the form[I|A], whereIis the identity matrix, andAis a generalized Cauchy matrix. Using Cauchy matrices, a construction is shown of maximal triangular arrays over GF(q), which are constant along diagonals in a Hankel matrix fashion, and with the property that every square subarray is a nonsingular matrix. By taking rectangular subarrays of the described triangles, it is possible to construct generator matrices[I|A]of maximum distance separable codes, whereAis a Hankel matrix. The parameters of the codes are(n,k,d), for1 leq n leq q+ 1, 1 leq k leq n, andd=n-k+1.