Список непериодических ожерелий над F_2, соответствующих неприводимых многочленов, орбит действия группы автоморфизмов G_n, порожденной нормальными базисами, и размерностей подпространств, порожденных корнями непривоимых многочленов (постоянны на орбитах). Например, для n=6 орбиты [[1, 5, 6, 9], [2, 8], [3, 7], [4]], и последняя строка: [6, 5, 4, 4], то есть [1, 5, 6, 9] имеют размерности 6 --- это нормальные полиномы---; далее [2, 8] - размерности 5, а [3, 7], и [4] - размерности 4. (Вычисление проделано Д.Пасечником (Сингапур)). 1 . 01 x^2 + x + 1 [[1]] [2] 1 . 001 x^3 + x^2 + 1 2 . 011 x^3 + x + 1 [[1], [2]] [3, 2] 1 . 0001 x^4 + x^3 + 1 2 . 0011 x^4 + x + 1 3 . 0111 x^4 + x^3 + x^2 + x + 1 [[1, 3], [2]] [4, 3] 1 . 00001 x^5 + x^4 + x^2 + x + 1 2 . 00011 x^5 + x^3 + x^2 + x + 1 3 . 00101 x^5 + x^3 + 1 4 . 00111 x^5 + x^4 + x^3 + x + 1 5 . 01011 x^5 + x^4 + x^3 + x^2 + 1 6 . 01111 x^5 + x^2 + 1 [[1, 4, 5], [2, 3, 6]] [5, 4] 1 . 000001 x^6 + x^5 + 1 2 . 000011 x^6 + x + 1 3 . 000101 x^6 + x^3 + 1 4 . 000111 x^6 + x^5 + x^3 + x^2 + 1 5 . 001011 x^6 + x^5 + x^4 + x + 1 6 . 001101 x^6 + x^5 + x^4 + x^2 + 1 7 . 001111 x^6 + x^4 + x^2 + x + 1 8 . 010111 x^6 + x^4 + x^3 + x + 1 9 . 011111 x^6 + x^5 + x^2 + x + 1 [[1, 5, 6, 9], [2, 8], [3, 7], [4]] [6, 5, 4, 4] 1 . 0000001 x^7 + x^6 + 1 2 . 0000011 x^7 + x^3 + x^2 + x + 1 3 . 0000101 x^7 + x^4 + x^3 + x^2 + 1 4 . 0001001 x^7 + x^5 + x^4 + x^3 + x^2 + x + 1 5 . 0000111 x^7 + x^6 + x^4 + x + 1 6 . 0001011 x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + 1 7 . 0001101 x^7 + x^6 + x^5 + x^4 + 1 8 . 0010011 x^7 + x^6 + x^3 + x + 1 9 . 0010101 x^7 + x^6 + x^5 + x^3 + x^2 + x + 1 10 . 0001111 x^7 + x^5 + x^4 + x^3 + 1 11 . 0010111 x^7 + x^3 + 1 12 . 0011011 x^7 + x^5 + x^2 + x + 1 13 . 0011101 x^7 + x + 1 14 . 0101011 x^7 + x^4 + 1 15 . 0011111 x^7 + x^6 + x^5 + x^4 + x^2 + x + 1 16 . 0101111 x^7 + x^6 + x^5 + x^2 + 1 17 . 0110111 x^7 + x^6 + x^4 + x^2 + 1 18 . 0111111 x^7 + x^5 + x^3 + x + 1 [[1, 5, 8, 9, 15, 16, 17], [2, 4, 14, 18, 3, 10, 12], [6], [7], [11], [13]] [7, 6, 4, 4, 3, 3] 1 . 00000001 x^8 + x^7 + x^2 + x + 1 2 . 00000011 x^8 + x^4 + x^3 + x + 1 3 . 00000101 x^8 + x^5 + x^3 + x + 1 4 . 00001001 x^8 + x^6 + x^5 + x^4 + x^2 + x + 1 5 . 00000111 x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 1 6 . 00001011 x^8 + x^7 + x^6 + x^5 + x^4 + x + 1 7 . 00001101 x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1 8 . 00010011 x^8 + x^7 + x^5 + x^3 + 1 9 . 00010101 x^8 + x^7 + x^6 + x^5 + x^2 + x + 1 10 . 00011001 x^8 + x^7 + x^5 + x^4 + 1 11 . 00100101 x^8 + x^7 + x^5 + x + 1 12 . 00001111 x^8 + x^6 + x^5 + x^3 + 1 13 . 00010111 x^8 + x^5 + x^4 + x^3 + 1 14 . 00011011 x^8 + x^6 + x^5 + x + 1 15 . 00011101 x^8 + x^5 + x^3 + x^2 + 1 16 . 00100111 x^8 + x^6 + x^5 + x^2 + 1 17 . 00101011 x^8 + x^6 + x^3 + x^2 + 1 18 . 00101101 x^8 + x^6 + x^5 + x^4 + x^3 + x + 1 19 . 00110101 x^8 + x^6 + x^4 + x^3 + x^2 + x + 1 20 . 00011111 x^8 + x^7 + x^6 + x^4 + x^2 + x + 1 21 . 00101111 x^8 + x^7 + x^3 + x^2 + 1 22 . 00110111 x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1 23 . 00111011 x^8 + x^7 + x^6 + x + 1 24 . 00111101 x^8 + x^7 + x^3 + x + 1 25 . 01010111 x^8 + x^7 + x^4 + x^3 + x^2 + x + 1 26 . 01011011 x^8 + x^7 + x^6 + x^3 + x^2 + x + 1 27 . 00111111 x^8 + x^4 + x^3 + x^2 + 1 28 . 01011111 x^8 + x^5 + x^4 + x^3 + x^2 + x + 1 29 . 01101111 x^8 + x^6 + x^5 + x^4 + 1 30 . 01111111 x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1 [[1, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 24, 25, 26, 30], [2, 4, 15, 13, 19, 27, 17, 29], [3, 14, 16, 28], [12, 18]] [8, 7, 6, 5] 1 . 000000001 x^9 + x^8 + 1 2 . 000000011 x^9 + x^4 + x^2 + x + 1 3 . 000000101 x^9 + x^6 + x^4 + x^3 + x^2 + x + 1 4 . 000001001 x^9 + x^7 + x^6 + x^3 + x^2 + x + 1 5 . 000010001 x^9 + x^7 + x^5 + x^4 + x^2 + x + 1 6 . 000000111 x^9 + x^8 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 7 . 000001011 x^9 + x^8 + x^7 + x^6 + x^4 + x^2 + 1 8 . 000001101 x^9 + x^8 + x^7 + x^6 + x^5 + x + 1 9 . 000010011 x^9 + x^8 + x^6 + x^3 + 1 10 . 000010101 x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + 1 11 . 000011001 x^9 + x^8 + x^6 + x^5 + x^4 + x + 1 12 . 000100011 x^9 + x^8 + x^5 + x + 1 13 . 000100101 x^9 + x^8 + x^4 + x + 1 14 . 000101001 x^9 + x^8 + x^4 + x^3 + x^2 + x + 1 15 . 000001111 x^9 + x^7 + x^6 + x^5 + x^4 + x^2 + 1 16 . 000010111 x^9 + x^6 + x^5 + x^3 + x^2 + x + 1 17 . 000011011 x^9 + x^7 + x^6 + x^4 + x^3 + x + 1 18 . 000011101 x^9 + x^6 + x^5 + x^3 + 1 19 . 000100111 x^9 + x^7 + x^2 + x + 1 20 . 000101011 x^9 + x^7 + x^6 + x^5 + x^4 + x^3 + 1 21 . 000101101 x^9 + x^7 + x^5 + x + 1 22 . 000110011 x^9 + x^6 + x^3 + x + 1 23 . 000110101 x^9 + x^7 + x^6 + x^4 + 1 24 . 000111001 x^9 + x^7 + x^5 + x^3 + x^2 + x + 1 25 . 001001011 x^9 + x^5 + x^3 + x^2 + 1 26 . 001001101 x^9 + x^5 + 1 27 . 001010011 x^9 + x^6 + x^5 + x^2 + 1 28 . 001010101 x^9 + x^7 + x^5 + x^2 + 1 29 . 000011111 x^9 + x^8 + x^7 + x^3 + x^2 + x + 1 30 . 000101111 x^9 + x^8 + x^6 + x^5 + x^3 + x + 1 31 . 000110111 x^9 + x^8 + x^7 + x^6 + x^2 + x + 1 32 . 000111011 x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x + 1 33 . 000111101 x^9 + x^8 + x^6 + x^5 + x^3 + x^2 + 1 34 . 001001111 x^9 + x^8 + x^7 + x^5 + x^4 + x^2 + 1 35 . 001010111 x^9 + x^8 + x^7 + x^5 + x^4 + x^3 + 1 36 . 001011011 x^9 + x^8 + x^5 + x^4 + 1 37 . 001011101 x^9 + x^8 + x^7 + x^6 + x^3 + x^2 + 1 38 . 001100111 x^9 + x^8 + x^6 + x^4 + x^3 + x + 1 39 . 001101011 x^9 + x^8 + x^6 + x^5 + 1 40 . 001101101 x^9 + x^8 + x^5 + x^4 + x^3 + x + 1 41 . 001110101 x^9 + x^8 + x^7 + x^2 + 1 42 . 010101011 x^9 + x^8 + x^7 + x^6 + x^3 + x + 1 43 . 000111111 x^9 + x^6 + x^5 + x^4 + x^3 + x^2 + 1 44 . 001011111 x^9 + x^7 + x^4 + x^3 + 1 45 . 001101111 x^9 + x^6 + x^5 + x^4 + x^2 + x + 1 46 . 001110111 x^9 + x^5 + x^4 + x + 1 47 . 001111011 x^9 + x^6 + x^4 + x^3 + 1 48 . 001111101 x^9 + x^7 + x^5 + x^4 + x^3 + x^2 + 1 49 . 010101111 x^9 + x^7 + x^4 + x^2 + 1 50 . 010110111 x^9 + x^4 + x^3 + x + 1 51 . 010111011 x^9 + x^4 + 1 52 . 001111111 x^9 + x^8 + x^4 + x^2 + 1 53 . 010111111 x^9 + x^8 + x^6 + x^3 + x^2 + x + 1 54 . 011011111 x^9 + x^8 + x^7 + x^5 + 1 55 . 011101111 x^9 + x^8 + x^7 + x^6 + x^4 + x^3 + 1 56 . 011111111 x^9 + x + 1 [[1, 7, 8, 9, 11, 13, 14, 29, 30, 31, 32, 33, 35, 36, 38, 40, 41, 42, 52, 53, 55], [2, 18, 16, 23, 20, 45, 47, 5, 19, 25, 26, 24, 44, 51, 28, 50, 48, 56, 3, 15, 22], [4, 27, 21, 17, 46, 49, 43], [6, 12, 34, 54, 37, 39, 10]] [9, 8, 6, 7]