Convolutional codes with maximum column sum rank for network streaming

The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We show that the column sum rank parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several column distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of super-regular matrices that preserve this property after multiplication with non-singular block diagonal matrices in the ground field.