Abstract
                                                                         Matroidal networks were introduced by Doughert yet   al.and   have   been   well   studied   in   the   recent past.  It  was  shown  that  a  network  has  a  scalar  linear  network coding  solution  if  and  only  if  it  is  matroidal  associated  with a  representable  matroid.  A  particularly  interesting  feature  of this  development  is  the  ability  to  construct  (scalar  and  vector)linearly  solvable   networks   using  certain   classes   of  matroids.Furthermore,  it  was   shown  through  the  connection  between network  coding  and  matroid  theory  that  linear  network  coding is  not  always  sufficient  for  general  network  coding  scenarios.The  current  work  attempts  to  establish  a  connection  between matroid   theory   and   network-error   correcting   and   detecting codes.  In  a  similar  vein  to  the  theory  connecting  matroids  and network   coding,   we   abstract   the   essential   aspects   of   linear network-error  detecting  codes  to  arrive  at  the  definition  of  a matroidal error detecting network(and similarly, a matroidal error correcting  networkabstracting  from  network-error  correcting codes).  An  acyclic  network  (with  arbitrary  sink  demands)  is then shown to possess a scalar linear error detecting (correcting)network  code  if  and  only  if  it  is  a  matroidal  error  detecting(correcting)  network  associated  with  a  representable  matroid.Therefore,   constructing   such   network-error   correcting   and detecting codes implies the construction of certain representable matroids  that  satisfy  some  special  conditions,  and  vice  versa.We  then  present  algorithms  that  enable  the  construction  of matroidal   error   detecting   and   correcting   networks   with   a specified   capability   of   network-error   correction.   Using   these construction   algorithms,   a   large   class   of   hitherto   unknown scalar  linearly  solvable  networks  with  multi source,  multicast,and  multiple- unicast  network-error  correcting  codes  is  made available   for   theoretical   use   and   practical   implementation,with   parameters,   such   as   number   of   information   symbols,number  of   sinks,  number  of   coding  nodes,  error   correcting capability,  and  so  on,  being arbitrary  but for  computing  power(for  the  execution  of  the  algorithms).  The  complexity  of  the construction  of  these  networks  is  shown  to  be  comparable  with the   complexity   of   existing   algorithms   that   design   multi cast scalar  linear  network-error  correcting  codes.  Finally,  we  also show that linear network coding is not sufficient for the general network-error   correction   (detection)   problem   with   arbitrary demands. In particular, for the same number of network errors,we show a network for which there is a nonlinear network-error detecting  code  satisfying  the  demands  at  the  sinks,  where as there   are   no   linear   network-error   detecting   codes   that   do the same.