On the invariants of a linear group of order 336
C. L. Mallows, Neil J.A. Sloane · Mathematical Proceedings of the Cambridge Philosophical Society · 1973
Abstract The polynomial invariants of a certain classical linear group of order 336 arise naturally in studying error-correcting codes over GF(7). An incomplete description of these invariants was given by Maschke in 1893. With the aid of the Poincaré series for this group, found by Edge in 1947, we complete Maschke's work by giving a unique representation for the invariants in terms of 12 basic invariants. A conjecture is made concerning the relationship between the Poincaré series and the degrees of the basic invariants for any linear group. A partial answer to this conjecture, due to E. C. Dade, is given.