  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YThe  [5XGAP[105X  package  [5XQDistRnd[105X implements a probabilistic algorithm for finding
  the  distance of a [23Xq[123X-ary quantum low-density parity-check code linear over a
  finite  field  [23XF=\mathop{\rm  GF}(q)[123X.  While  there  is  no guarantee of the
  performance  of  the  algorithm  (the existing bounds in the case of quantum
  LDPC codes are weak, see [14X3.2-2[114X), an empirical convergence criterion is given
  to  estimate  the probability that a minimum weight codeword has been found.
  Versions for CSS and regular stabilizer codes are given, see Section [14X4.1[114X[133X
  
  [33X[0;0YIn  addition,  a  format  for storing matrices associated with [23Xq[123X-ary quantum
  codes  is introduced and implemented, see Chapter [14X5[114X and Sec. [14X4.2[114X. The format
  is  based  on  the  well  establised MaTrix market eXchange (MTX) Coordinate
  format  developed  at  NIST, and is designed for full backward compatibility
  with this format. Thus, the files are readable by any software package which
  supports MTX.[133X
  
  [33X[0;0YThe  routines in the package are derived from the code originally written by
  one  of  the  authors (LPP). A related Covering Set algorithm has a provable
  performance  for  generic  (non-LDPC) quantum codes based on random matrices
  [DKP17]. Implemented version is a variant of the random [13Xinformation set[113X (IS)
  algorithm based on random column permutations and Gauss' elimination [Leo88]
  [Kru89] [CG90].[133X
  
  [33X[0;0YThe  [5XGAP[105X computer algebra system was chosen because of its excellent support
  for   linear   algebra   over  finite  fields.  Here  we  give  a  reference
  implementation  of  the  algorithm,  with  a  focus  on  matrix  formats and
  generality,  as  opposed  to  performance.  Nevertheless,  the  routines are
  sufficiently  fast  when  dealing  with codes of practically important block
  lengths [23Xn\lesssim 10^3[123X.[133X
  
