  A set of linearly constrained permutation matrices are proposed for
constructing a class of permutation codes. Making use of linear constraints
imposed on the permutation matrices, we can formulate a minimum Euclidian
distance decoding problem for the proposed class of permutation codes as a
linear programming (LP) problem. The main feature of this class of permutation
codes, called LP decodable permutation codes, is this LP decodability. It is
demonstrated that the LP decoding performance of the proposed class of
permutation codes is characterized by the vertices of the code polytope of the
code. Two types of linear constraints are discussed; one is structured
constraints and another is random constraints. The structured constraints such
as pure involution lead to an efficient encoding algorithm. On the other hand,
the random constraints enable us to use probabilistic methods for analyzing
several code properties such as the average cardinality and the average weight
distribution.
