Perfect codes in poset spaces and poset block spaces

The paper begins by giving a counter example to show that the algorithm for construction of new perfect poset codes from a given perfect poset code by removal of a coordinate as given by Lee (2004) [11] does not hold. The algorithm has been improved and generalized to obtain new perfect poset block codes from a given perfect poset block code. The modified necessary and sufficient conditions for the construction of new perfect poset codes have been derived as a particular case. A bound has been obtained on the height of poset Ps that turns a given π-code into r-perfect (Ps,π)-code. We show that there does not exist a poset which admits the binary Simplex code of order 3 to be a 2-perfect poset code. Also, all the poset structures which admit the extended ternary Golay code to be a 3-perfect poset code have been classified.