You may want to look at the outputs first.
all-irredpoly-out.txt is the output of all-irredpoly-demo.cc.
Generate all irreducible binary polynomials of given degree (from Lyndon words).
Indicate which are primitive (P) and normal (N).
The demo uses the functions from
all-irredpoly.h (fxt/src/bpol/all-irredpoly.h)
bit-necklace.h (fxt/src/bits/bit-necklace.h)
necklace2bitpol.h (fxt/src/bpol/necklace2bitpol.h)
bitpol-normal.cc (fxt/src/bpol/bitpol-normal.cc)
all-normalpoly-out.txt is the output of all-normalpoly-demo.cc.
Find all normal binary polynomials of degree n.
Print all corresponding multiplier matrices.
Cf. OEIS sequences A027362, A107222, and A272033.
The demo uses the functions from
all-irredpoly.h (fxt/src/bpol/all-irredpoly.h)
bit-necklace.h (fxt/src/bits/bit-necklace.h)
necklace2bitpol.h (fxt/src/bpol/necklace2bitpol.h)
normalbasis.h (fxt/src/bpol/normalbasis.h)
bitpol-normal.cc (fxt/src/bpol/bitpol-normal.cc)
bitmat-funcs.h (fxt/src/bmat/bitmat-funcs.h)
all-primpoly-srs-out.txt is the output of all-primpoly-srs-demo.cc.
Shift register sequences (SRS) for all primitive binary polynomials of given degree.
The sequences are maximum period sequences (m-sequences).
The demo uses the functions from
all-irredpoly.h (fxt/src/bpol/all-irredpoly.h)
lfsr.h (fxt/src/bpol/lfsr.h)
bitmat-circulant-out.txt is the output of bitmat-circulant-demo.cc.
Invertible circulant matrices over GF(2).
Cf. OEIS sequences A027362 and A003473.
The demo uses the functions from
bitmat-funcs.h (fxt/src/bmat/bitmat-funcs.h)
bitmat-inline.h (fxt/src/bmat/bitmat-inline.h)
bit-necklace.h (fxt/src/bits/bit-necklace.h)
bitpol-gcd.h (fxt/src/bpol/bitpol-gcd.h)
bitpolmod-arith.h (fxt/src/bpol/bitpolmod-arith.h)
bitmat-kronecker-out.txt is the output of bitmat-kronecker-demo.cc.
Irreducible polynomials and Kronecker products of their companion matrices.
The demo uses the functions from
bitmat-funcs.h (fxt/src/bmat/bitmat-funcs.h)
bitmat-inline.h (fxt/src/bmat/bitmat-inline.h)
bitpol-irred.h (fxt/src/bpol/bitpol-irred.h)
bitpol-primitive.h (fxt/src/bpol/bitpol-primitive.h)
bitpol-order.h (fxt/src/bpol/bitpol-order.h)
all-irredpoly.h (fxt/src/bpol/all-irredpoly.h)
factor.h (fxt/src/mod/factor.h)
mersenne.h (fxt/src/mod/mersenne.h)
bitpol-inverse-out.txt is the output of bitpol-inverse-demo.cc.
Modular inversion of binary polynomials via extended gcd (EGCD).
The demo uses the functions from
bitpol-gcd.h (fxt/src/bpol/bitpol-gcd.h)
bitpol-arith.h (fxt/src/bpol/bitpol-arith.h)
bitpolmod-arith.h (fxt/src/bpol/bitpolmod-arith.h)
bitpol-search-irred-out.txt is the output of bitpol-search-irred-demo.cc.
Find binary irreducible polynomials via exhaustive search.
The demo uses the functions from
bitpol-irred.h (fxt/src/bpol/bitpol-irred.h)
bitpol-irred-rabin.cc (fxt/src/bpol/bitpol-irred-rabin.cc)
bitpol-irred-ben-or.cc (fxt/src/bpol/bitpol-irred-ben-or.cc)
bitpol-spi.cc (fxt/src/bpol/bitpol-spi.cc)
bitpol-srp-out.txt is the output of bitpol-srp-demo.cc.
Generate all irreducible self-reciprocal binary polynomials of given degree.
Cf. OEIS sequences A000048, A175390, and A069925.
The demo uses the functions from
bitpol-srp.h (fxt/src/bpol/bitpol-srp.h)
all-irredpoly.h (fxt/src/bpol/all-irredpoly.h)
bitpolfactor-out.txt is the output of bitpolfactor-demo.cc.
Factorization of binary polynomials.
The demo uses the functions from
bitpol-factor.h (fxt/src/bpol/bitpol-factor.h)
bitpol-squarefree.h (fxt/src/bpol/bitpol-squarefree.h)
bitpol-degree.h (fxt/src/bpol/bitpol-degree.h)
bitpol-print.h (fxt/src/bpol/bitpol-print.h)
bitpolmodmult-out.txt is the output of bitpolmodmult-demo.cc.
Modular multiplication of binary polynomials.
The demo uses the functions from
bitpolmod-arith.h (fxt/src/bpol/bitpolmod-arith.h)
poly-tab.h (fxt/src/bpol/poly-tab.h)
bitpolmult-out.txt is the output of bitpolmult-demo.cc.
Multiplication of binary polynomials.
clhca-out.txt is the output of clhca-demo.cc.
Cyclic (additive) Linear Hybrid Cellular Automata (CLHCA).
The demo uses the functions from
clhca.h (fxt/src/bpol/clhca.h)
fcsr-out.txt is the output of fcsr-demo.cc.
Feedback Carry Shift Register.
The demo uses the functions from
fcsr.h (fxt/src/bpol/fcsr.h)
gf2n-out.txt is the output of gf2n-demo.cc.
Arithmetics over GF(2**n).
The demo uses the functions from
gf2n.h (fxt/src/bpol/gf2n.h)
gf2n.cc (fxt/src/bpol/gf2n.cc)
gf2n-matrix-out.txt is the output of gf2n-matrix-demo.cc.
Matrix representation of GF(2**n).
The demo uses the functions from
bitmat-funcs.h (fxt/src/bmat/bitmat-funcs.h)
bitmat-inline.h (fxt/src/bmat/bitmat-inline.h)
poly-tab.h (fxt/src/bpol/poly-tab.h)
gf2n-minpoly-out.txt is the output of gf2n-minpoly-demo.cc.
Minimal polynomials in GF(2**n).
The demo uses the functions from
gf2n.h (fxt/src/bpol/gf2n.h)
gf2n-minpoly.cc (fxt/src/bpol/gf2n-minpoly.cc)
gf2n-normal-out.txt is the output of gf2n-normal-demo.cc.
Arithmetics over GF(2**n): conversion to normal basis representation.
The demo uses the functions from
gf2n.h (fxt/src/bpol/gf2n.h)
gf2n.cc (fxt/src/bpol/gf2n.cc)
gf2n-solvequadratic-out.txt is the output of gf2n-solvequadratic-demo.cc.
Solving the reduced quadratic equation z^2+z==C over GF(2**n).
The demo uses the functions from
gf2n.h (fxt/src/bpol/gf2n.h)
gf2n-trace0-generators-out.txt is the output of gf2n-trace0-generators-demo.cc.
Count primitive elements with trace==0 in GF(2**n) (OEIS sequences A192211 and A152049).
The demo uses the functions from
gf2n.h (fxt/src/bpol/gf2n.h)
gf2n.cc (fxt/src/bpol/gf2n.cc)
bitpolmod-arith.h (fxt/src/bpol/bitpolmod-arith.h)
lfsr-out.txt is the output of lfsr-demo.cc.
Linear feedback shift register.
The demo uses the functions from
lfsr.h (fxt/src/bpol/lfsr.h)
poly-tab.h (fxt/src/bpol/poly-tab.h)
lfsr-fibonacci-out.txt is the output of lfsr-fibonacci-demo.cc.
Linear feedback shift register: Fibonacci setup with
right and left shift, polynomial c and reversed polynomial r.
lfsr-galois-out.txt is the output of lfsr-galois-demo.cc.
Linear feedback shift register: Galois setup with
right and left shift, polynomial c and reversed polynomial r.
lfsr-revbin-out.txt is the output of lfsr-revbin-demo.cc.
Generate all revbin pairs via a linear feedback shift register.
lfsr-trace0-generators-out.txt is the output of lfsr-trace0-generators-demo.cc.
Count primitive elements with trace==0 in GF(2^n).
Cf. OEIS sequences A192211 and A152049.
Fast method using class mersenne_coprime.
The demo uses the functions from
mersenne-coprime.h (fxt/src/bpol/mersenne-coprime.h)
lhca-out.txt is the output of lhca-demo.cc.
Linear Hybrid Cellular Automata (LHCA).
The demo uses the functions from
lhca.h (fxt/src/bpol/lhca.h)
lhca2poly-out.txt is the output of lhca2poly-demo.cc.
Convert minimum-weight LHCA rules to binary polynomials.
The demo uses the functions from
lhca.h (fxt/src/bpol/lhca.h)
bitpol-irred.h (fxt/src/bpol/bitpol-irred.h)
lowbit-lhca-out.txt is the output of lowbit-lhca-demo.cc.
Generate low-bit LHCA rules (LHCA:= Linear Hybrid Cellular Automaton).
The demo uses the functions from
lhca.h (fxt/src/bpol/lhca.h)
bitpol-irred.h (fxt/src/bpol/bitpol-irred.h)
bitpol-primitive.h (fxt/src/bpol/bitpol-primitive.h)
gf2n.h (fxt/src/bpol/gf2n.h)
minweight-lowbit-lhca-out.txt is the output of minweight-lowbit-lhca-demo.cc.
Generate minimal-weight low-bit LHCA rules (LHCA:= Linear Hybrid Cellular Automaton).
The demo uses the functions from
lhca.h (fxt/src/bpol/lhca.h)
bitcombcolex.h (fxt/src/bits/bitcombcolex.h)
bitpol-irred.h (fxt/src/bpol/bitpol-irred.h)
bitpol-primitive.h (fxt/src/bpol/bitpol-primitive.h)
gf2n.h (fxt/src/bpol/gf2n.h)
necklace2irred-out.txt is the output of necklace2irred-demo.cc.
Convert necklaces to binary polynomials, especially irreducible and primitive ones.
The demo uses the functions from
necklace2bitpol.h (fxt/src/bpol/necklace2bitpol.h)
bitcyclic-minmax.h (fxt/src/bits/bitcyclic-minmax.h)
bitcyclic-period.h (fxt/src/bits/bitcyclic-period.h)
normalbasis-out.txt is the output of normalbasis-demo.cc.
Multiplication with a normal basis for GF(2**n).
The demo uses the functions from
normalbasis.h (fxt/src/bpol/normalbasis.h)
normal-solvequadratic.h (fxt/src/bpol/normal-solvequadratic.h)
bitpol-normal.cc (fxt/src/bpol/bitpol-normal.cc)
normal-mult.cc (fxt/src/bpol/normal-mult.cc)
normal-primpoly.cc (fxt/src/bpol/normal-primpoly.cc)
normal-irredpoly.cc (fxt/src/bpol/normal-irredpoly.cc)
bitmat-funcs.h (fxt/src/bmat/bitmat-funcs.h)
normalpoly-dual-out.txt is the output of normalpoly-dual-demo.cc.
Find all normal binary polynomials of degree n and their duals.
The demo uses the functions from
normalpoly-dual.h (fxt/src/bpol/normalpoly-dual.h)
poly2lhca-out.txt is the output of poly2lhca-demo.cc.
Computation of the LHCA rule corresponding to an irreducible binary polynomial.
The demo uses the functions from
bitpol2lhca.cc (fxt/src/bpol/bitpol2lhca.cc)
bitpolmod-solvequadratic.h (fxt/src/bpol/bitpolmod-solvequadratic.h)
lhca.h (fxt/src/bpol/lhca.h)
primefact-out.txt is the output of primefact-demo.cc.
Finding odd primes that are composite as polynomials over GF(2).
The demo uses the functions from
bitpol-irred.h (fxt/src/bpol/bitpol-irred.h)
bitarray.h (fxt/src/ds/bitarray.h)
primes.h (fxt/src/mod/primes.h)
bithigh.h (fxt/src/bits/bithigh.h)
qmatrix-out.txt is the output of qmatrix-demo.cc.
Q-matrix and nullspace of (Q-id).
The demo uses the functions from
bitpol-factor.h (fxt/src/bpol/bitpol-factor.h)
berlekamp.cc (fxt/src/bpol/berlekamp.cc)
bitmat-funcs.h (fxt/src/bmat/bitmat-funcs.h)
bitmat-inline.h (fxt/src/bmat/bitmat-inline.h)