Usage of Method: Reed–Solomon Code
Appears in the following modes: “Constructive and linear” (464 times).
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| Incarnation | Mode | ||
|---|---|---|---|
| 1 | Linear OA(21, 2, F2, 1) (dual of [2, 1, 2]-code) | Constructive and linear | [i] |
| 2 | Linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code) | Constructive and linear | [i] |
| 3 | Linear OA(32, 3, F3, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)) | Constructive and linear | [i] |
| 4 | Linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code) | Constructive and linear | [i] |
| 5 | Linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)) | Constructive and linear | [i] |
| 6 | Linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)) | Constructive and linear | [i] |
| 7 | Linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code) | Constructive and linear | [i] |
| 8 | Linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)) | Constructive and linear | [i] |
| 9 | Linear OA(53, 5, F5, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)) | Constructive and linear | [i] |
| 10 | Linear OA(54, 5, F5, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,5)) | Constructive and linear | [i] |
| 11 | Linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code) | Constructive and linear | [i] |
| 12 | Linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)) | Constructive and linear | [i] |
| 13 | Linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)) | Constructive and linear | [i] |
| 14 | Linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)) | Constructive and linear | [i] |
| 15 | Linear OA(75, 7, F7, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,7)) | Constructive and linear | [i] |
| 16 | Linear OA(76, 7, F7, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,7)) | Constructive and linear | [i] |
| 17 | Linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code) | Constructive and linear | [i] |
| 18 | Linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)) | Constructive and linear | [i] |
| 19 | Linear OA(83, 8, F8, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)) | Constructive and linear | [i] |
| 20 | Linear OA(84, 8, F8, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)) | Constructive and linear | [i] |
| 21 | Linear OA(85, 8, F8, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,8)) | Constructive and linear | [i] |
| 22 | Linear OA(86, 8, F8, 6) (dual of [8, 2, 7]-code or 8-arc in PG(5,8)) | Constructive and linear | [i] |
| 23 | Linear OA(87, 8, F8, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,8)) | Constructive and linear | [i] |
| 24 | Linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code) | Constructive and linear | [i] |
| 25 | Linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)) | Constructive and linear | [i] |
| 26 | Linear OA(93, 9, F9, 3) (dual of [9, 6, 4]-code or 9-arc in PG(2,9) or 9-cap in PG(2,9)) | Constructive and linear | [i] |
| 27 | Linear OA(94, 9, F9, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,9)) | Constructive and linear | [i] |
| 28 | Linear OA(95, 9, F9, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,9)) | Constructive and linear | [i] |
| 29 | Linear OA(96, 9, F9, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,9)) | Constructive and linear | [i] |
| 30 | Linear OA(97, 9, F9, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,9)) | Constructive and linear | [i] |
| 31 | Linear OA(98, 9, F9, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,9)) | Constructive and linear | [i] |
| 32 | Linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code) | Constructive and linear | [i] |
| 33 | Linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)) | Constructive and linear | [i] |
| 34 | Linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)) | Constructive and linear | [i] |
| 35 | Linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)) | Constructive and linear | [i] |
| 36 | Linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)) | Constructive and linear | [i] |
| 37 | Linear OA(166, 16, F16, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)) | Constructive and linear | [i] |
| 38 | Linear OA(167, 16, F16, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)) | Constructive and linear | [i] |
| 39 | Linear OA(168, 16, F16, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)) | Constructive and linear | [i] |
| 40 | Linear OA(169, 16, F16, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)) | Constructive and linear | [i] |
| 41 | Linear OA(1610, 16, F16, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)) | Constructive and linear | [i] |
| 42 | Linear OA(1611, 16, F16, 11) (dual of [16, 5, 12]-code or 16-arc in PG(10,16)) | Constructive and linear | [i] |
| 43 | Linear OA(1612, 16, F16, 12) (dual of [16, 4, 13]-code or 16-arc in PG(11,16)) | Constructive and linear | [i] |
| 44 | Linear OA(1613, 16, F16, 13) (dual of [16, 3, 14]-code or 16-arc in PG(12,16)) | Constructive and linear | [i] |
| 45 | Linear OA(1614, 16, F16, 14) (dual of [16, 2, 15]-code or 16-arc in PG(13,16)) | Constructive and linear | [i] |
| 46 | Linear OA(1615, 16, F16, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,16)) | Constructive and linear | [i] |
| 47 | Linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code) | Constructive and linear | [i] |
| 48 | Linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)) | Constructive and linear | [i] |
| 49 | Linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)) | Constructive and linear | [i] |
| 50 | Linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)) | Constructive and linear | [i] |
| 51 | Linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)) | Constructive and linear | [i] |
| 52 | Linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)) | Constructive and linear | [i] |
| 53 | Linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)) | Constructive and linear | [i] |
| 54 | Linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)) | Constructive and linear | [i] |
| 55 | Linear OA(259, 25, F25, 9) (dual of [25, 16, 10]-code or 25-arc in PG(8,25)) | Constructive and linear | [i] |
| 56 | Linear OA(2510, 25, F25, 10) (dual of [25, 15, 11]-code or 25-arc in PG(9,25)) | Constructive and linear | [i] |
| 57 | Linear OA(2511, 25, F25, 11) (dual of [25, 14, 12]-code or 25-arc in PG(10,25)) | Constructive and linear | [i] |
| 58 | Linear OA(2512, 25, F25, 12) (dual of [25, 13, 13]-code or 25-arc in PG(11,25)) | Constructive and linear | [i] |
| 59 | Linear OA(2513, 25, F25, 13) (dual of [25, 12, 14]-code or 25-arc in PG(12,25)) | Constructive and linear | [i] |
| 60 | Linear OA(2514, 25, F25, 14) (dual of [25, 11, 15]-code or 25-arc in PG(13,25)) | Constructive and linear | [i] |
| 61 | Linear OA(2515, 25, F25, 15) (dual of [25, 10, 16]-code or 25-arc in PG(14,25)) | Constructive and linear | [i] |
| 62 | Linear OA(2516, 25, F25, 16) (dual of [25, 9, 17]-code or 25-arc in PG(15,25)) | Constructive and linear | [i] |
| 63 | Linear OA(2517, 25, F25, 17) (dual of [25, 8, 18]-code or 25-arc in PG(16,25)) | Constructive and linear | [i] |
| 64 | Linear OA(2518, 25, F25, 18) (dual of [25, 7, 19]-code or 25-arc in PG(17,25)) | Constructive and linear | [i] |
| 65 | Linear OA(2519, 25, F25, 19) (dual of [25, 6, 20]-code or 25-arc in PG(18,25)) | Constructive and linear | [i] |
| 66 | Linear OA(2520, 25, F25, 20) (dual of [25, 5, 21]-code or 25-arc in PG(19,25)) | Constructive and linear | [i] |
| 67 | Linear OA(2521, 25, F25, 21) (dual of [25, 4, 22]-code or 25-arc in PG(20,25)) | Constructive and linear | [i] |
| 68 | Linear OA(2522, 25, F25, 22) (dual of [25, 3, 23]-code or 25-arc in PG(21,25)) | Constructive and linear | [i] |
| 69 | Linear OA(2523, 25, F25, 23) (dual of [25, 2, 24]-code or 25-arc in PG(22,25)) | Constructive and linear | [i] |
| 70 | Linear OA(2524, 25, F25, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,25)) | Constructive and linear | [i] |
| 71 | Linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code) | Constructive and linear | [i] |
| 72 | Linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)) | Constructive and linear | [i] |
| 73 | Linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)) | Constructive and linear | [i] |
| 74 | Linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)) | Constructive and linear | [i] |
| 75 | Linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)) | Constructive and linear | [i] |
| 76 | Linear OA(276, 27, F27, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,27)) | Constructive and linear | [i] |
| 77 | Linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)) | Constructive and linear | [i] |
| 78 | Linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)) | Constructive and linear | [i] |
| 79 | Linear OA(279, 27, F27, 9) (dual of [27, 18, 10]-code or 27-arc in PG(8,27)) | Constructive and linear | [i] |
| 80 | Linear OA(2710, 27, F27, 10) (dual of [27, 17, 11]-code or 27-arc in PG(9,27)) | Constructive and linear | [i] |
| 81 | Linear OA(2711, 27, F27, 11) (dual of [27, 16, 12]-code or 27-arc in PG(10,27)) | Constructive and linear | [i] |
| 82 | Linear OA(2712, 27, F27, 12) (dual of [27, 15, 13]-code or 27-arc in PG(11,27)) | Constructive and linear | [i] |
| 83 | Linear OA(2713, 27, F27, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)) | Constructive and linear | [i] |
| 84 | Linear OA(2714, 27, F27, 14) (dual of [27, 13, 15]-code or 27-arc in PG(13,27)) | Constructive and linear | [i] |
| 85 | Linear OA(2715, 27, F27, 15) (dual of [27, 12, 16]-code or 27-arc in PG(14,27)) | Constructive and linear | [i] |
| 86 | Linear OA(2716, 27, F27, 16) (dual of [27, 11, 17]-code or 27-arc in PG(15,27)) | Constructive and linear | [i] |
| 87 | Linear OA(2717, 27, F27, 17) (dual of [27, 10, 18]-code or 27-arc in PG(16,27)) | Constructive and linear | [i] |
| 88 | Linear OA(2718, 27, F27, 18) (dual of [27, 9, 19]-code or 27-arc in PG(17,27)) | Constructive and linear | [i] |
| 89 | Linear OA(2719, 27, F27, 19) (dual of [27, 8, 20]-code or 27-arc in PG(18,27)) | Constructive and linear | [i] |
| 90 | Linear OA(2720, 27, F27, 20) (dual of [27, 7, 21]-code or 27-arc in PG(19,27)) | Constructive and linear | [i] |
| 91 | Linear OA(2721, 27, F27, 21) (dual of [27, 6, 22]-code or 27-arc in PG(20,27)) | Constructive and linear | [i] |
| 92 | Linear OA(2722, 27, F27, 22) (dual of [27, 5, 23]-code or 27-arc in PG(21,27)) | Constructive and linear | [i] |
| 93 | Linear OA(2723, 27, F27, 23) (dual of [27, 4, 24]-code or 27-arc in PG(22,27)) | Constructive and linear | [i] |
| 94 | Linear OA(2724, 27, F27, 24) (dual of [27, 3, 25]-code or 27-arc in PG(23,27)) | Constructive and linear | [i] |
| 95 | Linear OA(2725, 27, F27, 25) (dual of [27, 2, 26]-code or 27-arc in PG(24,27)) | Constructive and linear | [i] |
| 96 | Linear OA(2726, 27, F27, 26) (dual of [27, 1, 27]-code or 27-arc in PG(25,27)) | Constructive and linear | [i] |
| 97 | Linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code) | Constructive and linear | [i] |
| 98 | Linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)) | Constructive and linear | [i] |
| 99 | Linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)) | Constructive and linear | [i] |
| 100 | Linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)) | Constructive and linear | [i] |