Hadamard Matrices

• Introduction
• Equivalence Testing
  • IsHadamard(H): AlgMatElt → BoolElt
  • HadamardNormalize(H): AlgMatElt → AlgMatElt
  • HadamardCanonicalForm(H : parameters): AlgMatElt → AlgMatElt, AlgMatElt, AlgMatElt
  • HadamardInvariant(H): AlgMatElt → [ RngIntElt ]
  • IsHadamardEquivalent(H, J : parameters): AlgMatElt, AlgMatElt → BoolElt, AlgMatElt, AlgMatElt
  • HadamardMatrixToInteger(H): AlgMatElt → RngIntElt
  • HadamardMatrixFromInteger(x, n): RngIntElt, RngIntElt → AlgMatElt
  • Example: Hadamard Equivalence Testing
• Associated \(3\)-Designs
  • HadamardRowDesign(H, i): AlgMatElt, RngIntElt → Dsgn
  • HadamardColumnDesign(H, i): AlgMatElt, RngIntElt → Dsgn
  • Example: Hadamard Designs
• Automorphism Group
  • HadamardAutomorphismGroup(H : parameters): AlgMatElt → AlgMatElt
• Databases
  • HadamardDatabase() → DB
  • SkewHadamardDatabase() → DB
  • Matrix(D, n, k): DB, RngIntElt, RngIntElt → AlgMatElt
  • Matrices(D, n): DB, RngIntElt → [ AlgMatElt ]
  • DegreeRange(D): DB → RngIntElt, RngIntElt
  • Degrees(D): DB → [ RngIntElt ]
  • NumberOfMatrices(D, n): DB, RngIntElt → RngIntElt
  • Example: Hadamard Matrix Database
  • Updating the Databases
    • HadamardDatabaseInformation(D : parameters): DB → Rec
    • HadamardDatabaseInformationEmpty(: parameters) → Rec
    • UpdateHadamardDatabase(~R, S : parameters): Rec, SeqEnum
    • WriteHadamardDatabase(S, ~R): MonStgElt, Rec
    • WriteRawHadamardData(S, R): MonStgElt, Rec
    • SetVerbose("HadamardDB", v): MonStgElt, RngIntElt
    • Example: Updating the Hadamard Database