hlcd.operations.VectorGenerator

public class VectorGenerator extends Object

The generator of potential codewords in a sequential order. It uses the method getNextVector() to return the next valid vector. A valid vector is a vector that satisfies the minimum distance. A vector is of type long, which is a 64-bit value. In general, the vectors are going to be generated so that the first digit starts far-right, i.e., \(00...00\), \(00...01\), \(00...10\), \(00...11\), etc.

Here, indices are zero based. The important thought is that the zeroth column is the far-right column.

A quaternary digit is composed of a left digit and a right digit:

The representation of an quaternary digit
Quaternary Digit	Left Digit	Right Digit
\(0_4 \, = \, 00_2\)	\(0\)	\(0\)
\(1_4 \, = \, 01_2\)	\(0\)	\(1\)
\(\omega_4 \, = \, 10_2\)	\(1\)	\(0\)
\(\overline{\omega}_4 \, = \, 11_2\)	\(1\)	\(1\)

The \(i^{th}\) quaternary digit in a long datatype is given by: leftDigit = i * 2 + 1 and rightDigit = i * 2.

The implementation of this class only works for base \(4\) but can be modified to also include base \(2\).

Having minimum distance to be 0 or 1 will generate the exact set of valid vectors.

An important property in this class is RESTRICT_GENERATION. This should always be true as it will cut down the search space by an exponential factor when the base is \(4\). In addition, this requires to have the property ADD_IDENTITY to be true as well. The basic explanation is that the top row will be hardcoded so that it will have a weight of \(d\) consisting of \(1\)'s. The subvector in \(I\) will have a weight if \(1\) and the subvector in \(P\) will have \(d - 1\) as the weight, assuming the generator matrix is in the following form: \(G = \left[\begin{array} {@{}c|c@{}} I & P \end{array}\right]\). For each row, other than the top row in \(P\), the left-most nonzero digit will be \(1\) (not \(\omega\) nor \(\overline{\omega}\)). This construction guarantees that all possible inequivalent matrices will be generated. An explanation of how this is achieved can be found on page page 3 of Some optimal entanglement-assisted quantum codes constructed from quaternary Hermitian linear complementary dual codes by Masaaki Harada (Dec 2019).

TODO: When RESTRICT_GENERATION is true, the minimum distance must be less than or equal to \(3\). Implement \(d = 2\).

TODO: test binary implementation (regrading everything)

TODO: test quaternary implementation when having both RESTRICT_GENERATION and ADD_IDENTITY as false.

 //minimal example to execute this class:
 public static void main(String[] args) {
     System.out.println("Running VectorGenerator...");
     byte n = 20;
     byte k = 9;
     byte d = 9;
     byte minimumWeight = (byte) (d - 1);
     byte base = 4;
     boolean addIdentity = true;
     boolean restrictGeneration = true;
     long counter = 0;
     String ns = String.format("%" + 2 + "s", n + "");
     String ks = String.format("%" + 2 + "s", k + "");
     String ds = String.format("%" + 2 + "s", d + "");
     System.out.print("The code (" + ns + ", " + ks + ", " + ds + ") has ");
     VectorGenerator vg = new VectorGenerator(
         n, k, d, minimumWeight, base, addIdentity, restrictGeneration
     );
     while (true) {
         long vector = vg.getNextFullVector((byte) 0);
         if (vg.isCurrentSubvectorValid()) {
             counter++;
         } else {
             break;
         }
     }
     System.out.format("%,d%s\n", counter, " vectors to check.");
     System.out.println("VectorGenerator completed.");
 }

Since:: 1.8
Version:: 1.0 (February 1st, 2022)
Author:: Maysara Al Jumaily
See Also:: Long, Page 91 of the M.Sc. thesis, Page 93 of the M.Sc. thesis, Masaaki Harada's paper (Dec 2019)

Constructor Summary

Constructors

Constructor

Description

VectorGenerator(byte n, byte k, byte d, byte rhsWeight, byte base, boolean appendIdentity, boolean restrictGeneration)

Initializes the vector generator for the code.

VectorGenerator(byte n, byte k, byte d, byte rhsWeight, byte base, long startingSubvector, long resetPoint, boolean appendIdentity, boolean restrictGeneration)

Initializes the vector generator for the code.
Method Summary

Modifier and Type

Method

Description

long

getBase()

Returns the base of the code which could either be \(2\) or \(4\).

long

getCurrentFullVector(byte currentRow)

Returns the current subvector with the identity row attached.

long

getCurrentSubvector()

returns the current subvector without the identity subvector.

long

getMinimumRHSWeight()

Returns the minimum weight of the right-hand-side of a valid vector.

long

getNextFullVector(byte currentRow)

Returns the next subvector with the identity row attached.

long

getNextSubVector()

Returns the next subvector that satisfy the weight RHS_WEIGHT, which is \(d - 1\).

long

getResetPoint()

The current reset point which is a vector of Hamming weight of \(1\).

byte

getWeight(long vector, byte base)

Returns the weight of non-zero digits in the value passed.

boolean

isCurrentSubvectorValid()

Returns whether the current subvector is valid Hamming weight wise.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- VectorGenerator
  
  public VectorGenerator(byte n, byte k, byte d, byte rhsWeight, byte base, boolean appendIdentity, boolean restrictGeneration)
  
  Initializes the vector generator for the code. This particular constructor is used with base 4 only.
  
  Parameters:
  
  n - the length of the code
  
  k - the dimension of the code
  
  d - the minimum distance of the code
  
  rhsWeight - the Hamming weight of the subvector that is not a part of the identity submatrix. This must be \(d - 1\) assuming the identity matrix is appended
  
  base - the base of the code which could either be \(2\) or \(4\)
  
  appendIdentity - should the identity matrix be appended. This should always be true as it will significantly cut down the search space
  
  restrictGeneration - should a shortcut be used so that all the inequivalent generator matrices be generated This should always be true as it will further cut down the search space
- VectorGenerator
  
  public VectorGenerator(byte n, byte k, byte d, byte rhsWeight, byte base, long startingSubvector, long resetPoint, boolean appendIdentity, boolean restrictGeneration)
  
  Initializes the vector generator for the code. This particular constructor is used with base 4 only. This is used when a recursive call has been made to find the next codeword to be placed in the generator matrix.
  
  Parameters:
  
  n - the length of the code
  
  k - the dimension of the code
  
  d - the minimum distance of the code
  
  rhsWeight - the Hamming weight of the subvector that is not a part of the identity submatrix. This must be \(d - 1\) assuming the identity matrix is appended.
  
  base - the base of the code which could either be \(2\) or \(4\)
  
  startingSubvector - the starting position of the subvector that is not a part of the identity matrix
  
  resetPoint - a binary value that will have a weight of \(1\) where once reached, it denotes that some vectors can be skipped (assuming that the restriction generation property is on)
  
  appendIdentity - should the identity matrix be appended. This should always be true as it will significantly cut down the search space
  
  restrictGeneration - should a shortcut be used so that all the inequivalent generator matrices be generated This should always be true as it will further cut down the search space
Method Details
- getCurrentSubvector
  
  public long getCurrentSubvector()
  
  returns the current subvector without the identity subvector.
  
  Returns:
  
  the current subvector without the identity subvector
- getBase
  
  public long getBase()
  
  Returns the base of the code which could either be \(2\) or \(4\).
  
  Returns:
  
  the base of the code which could either be \(2\) or \(4\)
- getMinimumRHSWeight
  
  public long getMinimumRHSWeight()
  
  Returns the minimum weight of the right-hand-side of a valid vector.
  
  Returns:
  
  the minimum weight of the right-hand-side of a valid vector.
- getCurrentFullVector
  
  public long getCurrentFullVector(byte currentRow)
  
  Returns the current subvector with the identity row attached.
  
  Parameters:
  
  currentRow - the current row to place \(1\) in the valid position of the identity row portion
  
  Returns:
  
  The current subvector with the identity row attached
- getNextFullVector
  
  public long getNextFullVector(byte currentRow)
  
  Returns the next subvector with the identity row attached.
  
  Parameters:
  
  currentRow - the current row to place \(1\) in the valid position of the identity row portion
  
  Returns:
  
  The next vector with the identity row attached
- getNextSubVector
  
  public long getNextSubVector()
  
  Returns the next subvector that satisfy the weight RHS_WEIGHT, which is \(d - 1\).
  
  Returns:
  
  the next subvector that satisfy the weight RHS_WEIGHT, which is \(d - 1\)
- isCurrentSubvectorValid
  
  public boolean isCurrentSubvectorValid()
  
  Returns whether the current subvector is valid Hamming weight wise.
  
  Returns:
  
  true if the current subvector satisfy the Hamming weight, false otherwise
- getWeight
  
  public byte getWeight(long vector, byte base)
  
  Returns the weight of non-zero digits in the value passed. It will achieve that by going the binary representation of the value and increment a counter every time a digit (in base \(2\) or base \(4\) depending on the base passed) is not the digit \(0\).
  
  Parameters:
  
  vector - the vector to find the weight for
  
  base - the base the value should be treated as
  
  Returns:
  
  the number of non-zero digits in the vector passed
- getResetPoint
  
  public long getResetPoint()
  
  The current reset point which is a vector of Hamming weight of \(1\). It is used to generate vectors whose left-most on-zero digit is \(1\) (i.e., not 2 nor 3).
  
  Returns:
  
  the current reset point which is a vector of Hamming weight of \(1\)

Class VectorGenerator

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Details

VectorGenerator

VectorGenerator

Method Details

getCurrentSubvector

getBase

getMinimumRHSWeight

getCurrentFullVector

getNextFullVector

getNextSubVector

isCurrentSubvectorValid

getWeight

getResetPoint