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cyclgen


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 -- Loadable Function: H = cyclgen (N, P)
 -- Loadable Function: H = cyclgen (N, P, TYP)
 -- Loadable Function: [H, G] = cyclgen (...)
 -- Loadable Function: [H, G, K] = cyclgen (...)
     Produce the parity check and generator matrix of a cyclic code.
     The parity check matrix is returned as a M by N matrix,
     representing the [N,K] cyclic code. M is the order of the generator
     polynomial P and the message length K is given by `N - M'.

     The generator polynomial can either be a vector of ones and zeros,
     and length M representing,

          P(1) + P(2) * x + P(3) * x^2 + ... + P(M) * x^(m-1)

     The terms of the polynomial are stored least-significant term
     first.  Alternatively, P can be an integer representation of the
     same polynomial.

     The form of the parity check matrix is determined by TYP. If TYP
     is 'system', a systematic parity check matrix is produced. If TYP
     is 'nosys' and non-systematic parity check matrix is produced.

     If requested `cyclgen' also returns the K by N generator matrix G.

     See also: hammgen, gen2par, cyclpoly.



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Produce the parity check and generator matrix of a cyclic code.



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cyclpoly


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 -- Loadable Function: Y = cyclpoly (N, K)
 -- Loadable Function: Y = cyclpoly (N, K, OPT)
 -- Loadable Function: Y = cyclpoly (N, K, OPT, REP)
     This function returns the cyclic generator polynomials of the code
     [N,K]. By default the polynomial with the smallest weight is
     returned. However this behavior can be overridden with the OPT
     flag. Valid values of OPT are:

    `"all"'
          Returns all of the polynomials of the code [N,K]

    `"min"'
          Returns the polynomial of minimum weight of the code [N,K]

    `"max"'
          Returns the polynomial of the maximum weight of the code [N,K]

    L
          Returns the polynomials having exactly the weight L

     The polynomials are returns as row-vectors in the variable Y. Each
     row of Y represents a polynomial with the least-significant term
     first. The polynomials can be returned with an integer
     representation if REP is `"integer"'. The default behavior is
     given if REP is `"polynomial"'.

     See also: gf, isprimitive.



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This function returns the cyclic generator polynomials of the code
[N,K].



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genqamdemod


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 -- Loadable Function: Y = genqamdemod (X, C)
     General quadrature amplitude demodulation. The complex envelope
     quadrature amplitude modulated signal X is demodulated using a
     constellation mapping specified by the 1D vector C.


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General quadrature amplitude demodulation.



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gf


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 -- Loadable Function: Y = gf (X)
 -- Loadable Function: Y = gf (X, M)
 -- Loadable Function: Y = gf (X, M, PRIMPOLY)
     Creates a Galois field array GF(2^M) from the matrix X. The Galois
     field has 2^M elements, where M must be between 1 and 16.  The
     elements of X must be between 0 and 2^M - 1. If M is undefined it
     defaults to the value 1.

     The primitive polynomial to use in the creation of Galois field
     can be specified with the PRIMPOLY variable. If this is undefined
     a default primitive polynomial is used. It should be noted that
     the primitive polynomial must be of the degree M and it must be
     irreducible.

     The output of this function is recognized as a Galois field by
     Octave and other matrices will be converted to the same Galois
     field when used in an arithmetic operation with a Galois field.

     See also: isprimitive, primpoly.



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Creates a Galois field array GF(2^M) from the matrix X.



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isprimitive


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 -- Loadable Function: Y = isprimitive (A)
     Returns 1 is the polynomial represented by A is a primitive
     polynomial of GF(2). Otherwise it returns zero.

     See also: gf, primpoly.



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Returns 1 is the polynomial represented by A is a primitive polynomial
of GF(2).



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primpoly


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 -- Loadable Function: Y = primpoly (M)
 -- Loadable Function: Y = primpoly (M, OPT)
 -- Loadable Function: Y = primpoly (..., "nodisplay")
     Finds the primitive polynomials in GF(2^M).

     The first form of this function returns the default primitive
     polynomial of GF(2^M). This is the minimum primitive polynomial of
     the field. The polynomial representation is printed and an integer
     representation of the polynomial is returned

     The call `primpoly (M, OPT)' returns one or more primitive
     polynomials. The output of the function is dependent of the value
     of OPT.  Valid values of OPT are:

    `"all"'
          Returns all of the primitive polynomials of GF(2^M)

    `"min"'
          Returns the minimum primitive polynomial of GF(2^M)

    `"max"'
          Returns the maximum primitive polynomial of GF(2^M)

    K
          Returns the primitive polynomials having exactly K non-zero
          terms

     The call `primpoly (..., "nodisplay")' disables the output of the
     polynomial forms of the primitives. The return value is not
     affected.

     See also: gf, isprimitive.



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Finds the primitive polynomials in GF(2^M).



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syndtable


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 -- Loadable Function: T = syndtable (H)
     Create the syndrome decoding table from the parity check matrix H.
     Each row of the returned matrix T represents the error vector in a
     received symbol for a certain syndrome. The row selected is
     determined by a conversion of the syndrome to an integer
     representation, and using this to reference each row of T.

     See also: hammgen, cyclgen.



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Create the syndrome decoding table from the parity check matrix H.





