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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.





