  The conventional theory of linear network coding (LNC) is only over acyclic
networks. Convolutional network coding (CNC) applies to all networks. It is
also a form of LNC, but the linearity is w.r.t. the ring of rational power
series rather than the field of data symbols. CNC has been generalized to LNC
w.r.t. any discrete valuation ring (DVR) in order for flexibility in
applications. For a causal DVR-based code, all possible source-generated
messages form a free module, while incoming coding vectors to a receiver span
the \emph{received submodule}. An existing \emph{time-invariant decoding}
algorithm is at a delay equal to the largest valuation among all invariant
factors of the received submodule. This intrinsic algebraic attribute is herein
proved to be the optimal decoding delay. Meanwhile, \emph{time-variant
decoding} is formulated. The meaning of time-invariant decoding delay gets a
new interpretation through being a special case of the time-variant
counterpart. The optimal delay turns out to be the same for time-variant
decoding, but the decoding algorithm is more flexible in terms of decodability
check and decoding matrix design. All results apply, in particular, to CNC.
