We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the qu...

In this paper, a generic method to derive subsystem codes from existing subsystem codes is given that allows one to trade the dimensions of subsystem and co-subsystem while maintaining or improving the minimum distance. As a consequence, it is shown that all pure MDS subsystem codes are derived from MDS stabilizer codes. Furthermore, a simple construction of pure MDS subsystem codes is obtained...

A bstract We investigate the spontaneous breaking of subsystem symmetries directly in context continuum field theories by calculating correlation function charged operators. Our methods confirm lack symmetry some existing with symmetries, as had previously been established based on a careful analysis spectrum. present novel theory constructions that do exhibit whenever allowed general principle...

bin(k-1 ;n,p) = L n p xqn-x, the cumulative binomial function. k-1 ( ) x=o x C=the total of the cost of the subsystem itself plus the expected cost due to subsystem failure c1 = loss due to failure of the subsystem c3 =cost of a one module subsystem capable of full output c4 =cost of a module in a k-out-of-n:G (good) subsystem when k is fixed g(k) = the function relating cost of the subsystem t...

Impwtant aspects of mission operations for spacecraft (S/C) sent to explore outer space are: engineering subsystem performance analysis, characterization, and commanding, all involving a substantial amount of human resources and time. Recent efforts have brought about several productivity enhancement measures within the mission operations area that incluck the streamlining of the operations pro...