Information on Result #606340
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)), using Reed–Solomon code RS(4,7)
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(730, 35, F7, 23) (dual of [35, 5, 24]-code) | [i] | Generalized (u, u+v)-Construction | |
| 2 | Linear OA(730, 35, F7, 23) (dual of [35, 5, 24]-code) | [i] | ||
| 3 | Linear OA(730, 36, F7, 23) (dual of [36, 6, 24]-code) | [i] | ||
| 4 | Linear OA(725, 30, F7, 19) (dual of [30, 5, 20]-code) | [i] | ||
| 5 | Linear OA(725, 30, F7, 19) (dual of [30, 5, 20]-code) | [i] | ||
| 6 | Linear OA(721, 30, F7, 14) (dual of [30, 9, 15]-code) | [i] | ||
| 7 | Linear OA(719, 25, F7, 14) (dual of [25, 6, 15]-code) | [i] | ||
| 8 | Linear OA(753, 57, F7, 45) (dual of [57, 4, 46]-code) | [i] | Juxtaposition | |
| 9 | Linear OA(759, 63, F7, 48) (dual of [63, 4, 49]-code) | [i] | ||
| 10 | Linear OA(760, 64, F7, 49) (dual of [64, 4, 50]-code) | [i] | ||
| 11 | Linear OA(7103, 107, F7, 87) (dual of [107, 4, 88]-code) | [i] | ||
| 12 | Linear OA(7110, 114, F7, 91) (dual of [114, 4, 92]-code) | [i] | ||
| 13 | Linear OA(761, 65, F7, 51) (dual of [65, 4, 52]-code) | [i] | ||
| 14 | Linear OA(763, 67, F7, 52) (dual of [67, 4, 53]-code) | [i] | ||
| 15 | Linear OA(757, 65, F7, 39) (dual of [65, 8, 40]-code) | [i] | Concatenation of Two Codes | |
| 16 | Linear OA(762, 70, F7, 43) (dual of [70, 8, 44]-code) | [i] | ||
| 17 | Linear OA(767, 75, F7, 47) (dual of [75, 8, 48]-code) | [i] | ||
| 18 | Linear OA(775, 85, F7, 51) (dual of [85, 10, 52]-code) | [i] | ||
| 19 | Linear OA(772, 80, F7, 51) (dual of [80, 8, 52]-code) | [i] | ||
| 20 | Linear OA(769, 75, F7, 51) (dual of [75, 6, 52]-code) | [i] | ||
| 21 | Linear OA(780, 90, F7, 55) (dual of [90, 10, 56]-code) | [i] | ||
| 22 | Linear OA(777, 85, F7, 55) (dual of [85, 8, 56]-code) | [i] | ||
| 23 | Linear OA(774, 80, F7, 55) (dual of [80, 6, 56]-code) | [i] | ||
| 24 | Linear OA(785, 95, F7, 59) (dual of [95, 10, 60]-code) | [i] | ||
| 25 | Linear OA(779, 85, F7, 59) (dual of [85, 6, 60]-code) | [i] | ||
| 26 | Linear OA(793, 105, F7, 63) (dual of [105, 12, 64]-code) | [i] | ||
| 27 | Linear OA(790, 100, F7, 63) (dual of [100, 10, 64]-code) | [i] | ||
| 28 | Linear OA(798, 110, F7, 67) (dual of [110, 12, 68]-code) | [i] | ||
| 29 | Linear OA(795, 105, F7, 67) (dual of [105, 10, 68]-code) | [i] | ||
| 30 | Linear OA(7103, 115, F7, 71) (dual of [115, 12, 72]-code) | [i] | ||
| 31 | Linear OA(7100, 110, F7, 71) (dual of [110, 10, 72]-code) | [i] | ||
| 32 | Linear OA(797, 105, F7, 71) (dual of [105, 8, 72]-code) | [i] | ||
| 33 | Linear OA(794, 100, F7, 71) (dual of [100, 6, 72]-code) | [i] | ||
| 34 | Linear OA(7108, 120, F7, 75) (dual of [120, 12, 76]-code) | [i] | ||
| 35 | Linear OA(7105, 115, F7, 75) (dual of [115, 10, 76]-code) | [i] | ||
| 36 | Linear OA(7102, 110, F7, 75) (dual of [110, 8, 76]-code) | [i] | ||
| 37 | Linear OA(799, 105, F7, 75) (dual of [105, 6, 76]-code) | [i] | ||
| 38 | Linear OA(7110, 120, F7, 79) (dual of [120, 10, 80]-code) | [i] | ||
| 39 | Linear OA(723, 30, F7, 16) (dual of [30, 7, 17]-code) | [i] | Construction X with Cyclic Codes | |
| 40 | Linear OA(722, 30, F7, 15) (dual of [30, 8, 16]-code) | [i] | ||
| 41 | Linear OA(740, 63, F7, 21) (dual of [63, 23, 22]-code) | [i] | ||
| 42 | Linear OA(744, 64, F7, 25) (dual of [64, 20, 26]-code) | [i] | ||
| 43 | Linear OA(798, 107, F7, 71) (dual of [107, 9, 72]-code) | [i] | ||
| 44 | Linear OA(795, 104, F7, 69) (dual of [104, 9, 70]-code) | [i] | Construction XX with Cyclic Codes | |
| 45 | Linear OA(726, 31, F7, 20) (dual of [31, 5, 21]-code) | [i] | ||
| 46 | Linear OA(724, 31, F7, 17) (dual of [31, 7, 18]-code) | [i] | ||
| 47 | Linear OA(723, 31, F7, 16) (dual of [31, 8, 17]-code) | [i] | ||
| 48 | Linear OA(746, 67, F7, 25) (dual of [67, 21, 26]-code) | [i] | ||
| 49 | Linear OA(733, 62, F7, 18) (dual of [62, 29, 19]-code) | [i] | ||
| 50 | Linear OA(731, 58, F7, 18) (dual of [58, 27, 19]-code) | [i] | ||
| 51 | Linear OA(734, 61, F7, 19) (dual of [61, 27, 20]-code) | [i] | ||
| 52 | Linear OA(738, 65, F7, 20) (dual of [65, 27, 21]-code) | [i] | ||
| 53 | Linear OA(730, 56, F7, 18) (dual of [56, 26, 19]-code) | [i] | ||
| 54 | Linear OA(733, 59, F7, 19) (dual of [59, 26, 20]-code) | [i] | ||
| 55 | Linear OA(736, 62, F7, 20) (dual of [62, 26, 21]-code) | [i] | ||
| 56 | Linear OA(740, 66, F7, 21) (dual of [66, 26, 22]-code) | [i] | ||
| 57 | Linear OA(752, 73, F7, 29) (dual of [73, 21, 30]-code) | [i] | ||
| 58 | Linear OA(757, 71, F7, 36) (dual of [71, 14, 37]-code) | [i] | ||
| 59 | Linear OA(729, 62, F7, 15) (dual of [62, 33, 16]-code) | [i] | ||
| 60 | Linear OA(729, 62, F7, 15) (dual of [62, 33, 16]-code) | [i] | ||
| 61 | Linear OA(744, 71, F7, 23) (dual of [71, 27, 24]-code) | [i] | ||
| 62 | Linear OA(746, 73, F7, 24) (dual of [73, 27, 25]-code) | [i] | ||
| 63 | Linear OA(743, 69, F7, 23) (dual of [69, 26, 24]-code) | [i] | ||
| 64 | Linear OA(752, 128, F7, 21) (dual of [128, 76, 22]-code) | [i] | ||
| 65 | Linear OA(751, 126, F7, 21) (dual of [126, 75, 22]-code) | [i] | ||
| 66 | Linear OA(750, 124, F7, 21) (dual of [124, 74, 22]-code) | [i] | ||
| 67 | Linear OA(792, 16843, F7, 19) (dual of [16843, 16751, 20]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 68 | Linear OA(791, 16841, F7, 19) (dual of [16841, 16750, 20]-code) | [i] | ||
| 69 | Linear OA(7110, 2417, F7, 30) (dual of [2417, 2307, 31]-code) | [i] | ||
| 70 | Linear OA(763, 2418, F7, 17) (dual of [2418, 2355, 18]-code) | [i] | ||
| 71 | Linear OA(7104, 378, F7, 35) (dual of [378, 274, 36]-code) | [i] | ||
| 72 | Linear OA(7103, 376, F7, 35) (dual of [376, 273, 36]-code) | [i] | ||
| 73 | Linear OA(795, 369, F7, 33) (dual of [369, 274, 34]-code) | [i] | ||
| 74 | Linear OA(794, 367, F7, 33) (dual of [367, 273, 34]-code) | [i] | ||
| 75 | Linear OA(785, 358, F7, 31) (dual of [358, 273, 32]-code) | [i] | ||
| 76 | Linear OA(767, 376, F7, 21) (dual of [376, 309, 22]-code) | [i] | ||
| 77 | Linear OA(759, 369, F7, 19) (dual of [369, 310, 20]-code) | [i] | ||
| 78 | Linear OA(758, 367, F7, 19) (dual of [367, 309, 20]-code) | [i] | ||
| 79 | Linear OA(749, 358, F7, 17) (dual of [358, 309, 18]-code) | [i] | ||
| 80 | Linear OA(796, 105, F7, 69) (dual of [105, 9, 70]-code) | [i] | ||
| 81 | Linear OA(747, 122, F7, 20) (dual of [122, 75, 21]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 82 | Linear OA(794, 103, F7, 68) (dual of [103, 9, 69]-code) | [i] | ||
| 83 | Linear OA(736, 54, F7, 24) (dual of [54, 18, 25]-code) | [i] | ||
| 84 | Linear OA(728, 55, F7, 17) (dual of [55, 27, 18]-code) | [i] | ||
| 85 | Linear OA(727, 56, F7, 16) (dual of [56, 29, 17]-code) | [i] | ||
| 86 | Linear OA(756, 74, F7, 33) (dual of [74, 18, 34]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 87 | Linear OA(754, 72, F7, 32) (dual of [72, 18, 33]-code) | [i] | ||
| 88 | Linear OA(746, 72, F7, 24) (dual of [72, 26, 25]-code) | [i] | ||
| 89 | Linear OA(735, 61, F7, 19) (dual of [61, 26, 20]-code) | [i] | ||
| 90 | Linear OA(765, 75, F7, 45) (dual of [75, 10, 46]-code) | [i] | Construction X with Varšamov Bound | |
| 91 | Linear OA(773, 83, F7, 51) (dual of [83, 10, 52]-code) | [i] | ||
| 92 | Linear OA(785, 102, F7, 56) (dual of [102, 17, 57]-code) | [i] | ||
| 93 | Linear OA(789, 106, F7, 59) (dual of [106, 17, 60]-code) | [i] | ||
| 94 | Linear OA(790, 106, F7, 60) (dual of [106, 16, 61]-code) | [i] | ||
| 95 | Linear OA(792, 107, F7, 62) (dual of [107, 15, 63]-code) | [i] | ||
| 96 | Linear OA(785, 107, F7, 54) (dual of [107, 22, 55]-code) | [i] | ||