Calculates the generator polynomials for a BCH coder. Called with no input
arguments bchpoly returns a list of all of the valid BCH codes for
the codeword length 7, 15, 31, 63, 127, 255 and 511. A three column matrix
is returned with each row representing a separate valid BCH code. The first
column is the codeword length, the second the message length and the third
the error correction capability of the code.
Called with a single input argument, bchpoly returns the valid BCH
codes for the specified codeword length n. The output format is the
same as above.
When called with two or more arguments, bchpoly calculates the
generator polynomial of a particular BCH code. The generator polynomial
is returned in p as a vector representation of a polynomial in
GF(2). The terms of the polynomial are listed least-significant term
first.
The desired BCH code can be specified by its codeword length n and its message length k. Alternatively, the primitive polynomial over which to calculate the polynomial can be specified as prim. If a vector representation of the primitive polynomial is given, then prim can be specified as the first argument of two arguments, or as the third argument. However, if an integer representation of the primitive polynomial is used, then the primitive polynomial must be specified as the third argument.
When called with two or more arguments, bchpoly can also return the
factors f of the generator polynomial p, the cyclotomic coset
for the Galois field over which the BCH code is calculated, the parity
check matrix par and the error correction capability t. It
should be noted that the parity check matrix is calculated with
cyclgen and limitations in this function means that the parity
check matrix is only available for codeword length up to 63. For
codeword length longer than this par returns an empty matrix.
With a string argument probe defined, the action of bchpoly
is to calculate the error correcting capability of the BCH code defined
by n, k and prim and return it in p. This is
similar to a call to bchpoly with zero or one argument, except that
only a single code is checked. Any string value for probe will
force this action.
In general the codeword length n can be expressed as
2^m-1, where m is an integer. However, if
[n,k] is a valid BCH code, then a shortened BCH code of
the form [n-x,k-x] can be created with the
same generator polynomial
See also: cyclpoly, encode, decode, cosets.
Package: communications