-e Generated file: doc for tables in the data/ directory ----- all-irred-self-dual.txt: # # Complete list of binary irreducible normal polynomials # whose roots are a self-dual basis, up to degree 19. # There are no such polynomials with degree a multiple of 4. # Primitive polynomials are marked by a P. #. ----- all-irred-srp.txt: # # Complete list of binary irreducible self-reciprocal polynomials (SRP) # up to degree 22. The only SRP of odd degree (1+x) is omitted. # The number after the percent sign equals (2^(n/2)+1)/r where # r is the order of the polynomial with degree n. # #. ----- all-irredpoly.txt: # # Complete list of binary irreducible polynomials # up to degree 11 #. ----- all-lowblock-irredpoly-short.txt: # # Complete list of the irreducible polynomials over GF(2) # of the form x^d + \sum_{k=0}^{q}{x^q} # where q # e is the largest power of two that divides n # # Examples: # n=6: [x^6+1] = ( [x+1]*[x^2+x+1] )^2 # n=15: [x^15+1] = ( [x+1]*[x^2+x+1][x^4+x+1]*[x^4+x^3+1]*[x^4+x^3+x^2+x+1] )^1 #. ----- pseudo-13mod24.txt: # Composites n<2^32 of the form 24k+13 for which # H_{(n-1)/4}==0 (where H_0=1, H_1=2, H_{k}=4*H_{k-1}-H_{k-2}) # together with up to five bases a<1000 they are strong pseudoprimes to. #. ----- pseudo-19mod24.txt: # Composites n<2^32 of the form 24k+19 for which # U_{(n+1)/4}==0 (where U_0=0, U_1=1, U_{k}=4*U_{k-1}-U_{k-2}) # together with bases a<10^5 they are strong pseudoprimes to. # Maximal 5 bases are listed with each number. #. ----- pseudo-1mod24.txt: # Composites n<2^32 of the form 24k+1 for which # U_{(n-1)/4}==0 (where U_0=0, U_1=1, U_{k}=4*U_{k-1}-U_{k-2}) # together with bases a<100 they are strong pseudoprimes to. # Maximal 5 bases are listed with each number. #. ----- pseudo-5mod6.txt: # Composites n<2^32 of the form 6k+5 for which # U_{(n+s)/2}==0 (where U_0=0, U_1=1, U_{k}=4*U_{k-1}-U_{k-2} # and s=1 if n%4=1, s=-1 if n%4=3). # n followed by the smallest bases a<1000 they are strong pseudoprimes to # (up to six bases are given). #. ----- pseudo-7mod24.txt: # Composites n<2^32 of the form 24k+7 for which # H_{(n+1)/4}==0 (where H_0=1, H_1=2, H_{k}=4*H_{k-1}-H_{k-2}) # together with bases a<10^5 they are SPPs to. # Maximal 5 SPP bases are listed with each number. #. ----- pseudo-spp23.txt: # Odd composite n<2^32 which are strong pseudoprimes to both bases 2, and 3. # There are 104 entries in the list. # Modulo 12 the distribution is: # n%12 num # 1 75 # 5 9 # 7 18 # 11 2 #. ----- rand-primpoly.txt: # # 'random' binary primitive polynomials #. ----- rand32-hex-primpoly.txt: # # 100 'random' degree-32 binary primitive polynomials # as hexadecimal numbers with leading coefficient omitted (!) # # The polynomials are those given in rand32-primpoly.txt #. ----- rand32-primpoly.txt: # # 100 'random' degree-32 binary primitive polynomials #. ----- rand64-hex-primpoly.txt: # # 100 'random' degree-64 binary primitive polynomials # as hexadecimal numbers with leading coefficient omitted (!) # # The polynomials are those given in rand64-primpoly.txt #. ----- rand64-primpoly.txt: # # 100 'random' degree-64 binary primitive polynomials #. ----- root-sums.txt: # Aperiodic sums of roots of unity that are zero. # Format: # k: [bit-string] n [subset] # k is the rank of the necklace in lex order # (starting with k=1 for the all-zero word), # n is the length of the necklace. # # For example, the line # 6: ...11..1..11 12 0 1 4 7 8 # says that Z:=w^0+w^1+w^4+w^7+w^8==0 where w := exp(2*Pi*I/12) # # Such sums Z exist for the following n: # n: 1, 12, 18, 20, 24, 28, 30, 36, 40, 42, 44, 45, # numof(Z) 1, 2, 24, 6, 236, 18, 3768, 20384, 7188, 227784, 186, 481732448, # The list is complete for 1