Information on Result #657139
Linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
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
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(726, 351, F7, 9) (dual of [351, 325, 10]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(733, 2409, F7, 9) (dual of [2409, 2376, 10]-code) | [i] | ||
| 3 | Linear OA(740, 16815, F7, 9) (dual of [16815, 16775, 10]-code) | [i] | ||
| 4 | Linear OA(747, 117657, F7, 9) (dual of [117657, 117610, 10]-code) | [i] | ||
| 5 | Linear OA(754, 823551, F7, 9) (dual of [823551, 823497, 10]-code) | [i] | ||
| 6 | Linear OA(761, 5764809, F7, 9) (dual of [5764809, 5764748, 10]-code) | [i] | ||
| 7 | Linear OA(723, 351, F7, 8) (dual of [351, 328, 9]-code) | [i] | ||
| 8 | Linear OA(729, 2409, F7, 8) (dual of [2409, 2380, 9]-code) | [i] | ||
| 9 | Linear OA(735, 16815, F7, 8) (dual of [16815, 16780, 9]-code) | [i] | ||
| 10 | Linear OA(741, 117657, F7, 8) (dual of [117657, 117616, 9]-code) | [i] | ||
| 11 | Linear OA(747, 823551, F7, 8) (dual of [823551, 823504, 9]-code) | [i] | ||
| 12 | Linear OA(753, 5764809, F7, 8) (dual of [5764809, 5764756, 9]-code) | [i] | ||
| 13 | Linear OA(747, 56, F7, 34) (dual of [56, 9, 35]-code) | [i] | Generalized (u, u+v)-Construction | |
| 14 | Linear OA(750, 60, F7, 34) (dual of [60, 10, 35]-code) | [i] | ||
| 15 | Linear OA(744, 56, F7, 29) (dual of [56, 12, 30]-code) | [i] | ||
| 16 | Linear OA(744, 56, F7, 29) (dual of [56, 12, 30]-code) | [i] | ||
| 17 | Linear OA(742, 56, F7, 27) (dual of [56, 14, 28]-code) | [i] | ||
| 18 | Linear OA(744, 59, F7, 26) (dual of [59, 15, 27]-code) | [i] | ||
| 19 | Linear OA(734, 56, F7, 19) (dual of [56, 22, 20]-code) | [i] | ||
| 20 | Linear OA(737, 60, F7, 19) (dual of [60, 23, 20]-code) | [i] | ||
| 21 | Linear OA(754, 58, F7, 46) (dual of [58, 4, 47]-code) | [i] | Juxtaposition | |
| 22 | Linear OA(761, 65, F7, 50) (dual of [65, 4, 51]-code) | [i] | ||
| 23 | Linear OA(762, 66, F7, 51) (dual of [66, 4, 52]-code) | [i] | ||
| 24 | Linear OA(7104, 108, F7, 88) (dual of [108, 4, 89]-code) | [i] | ||
| 25 | Linear OA(762, 66, F7, 52) (dual of [66, 4, 53]-code) | [i] | ||
| 26 | Linear OA(764, 68, F7, 53) (dual of [68, 4, 54]-code) | [i] | ||
| 27 | Linear OA(75, 11, F7, 4) (dual of [11, 6, 5]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 28 | Linear OA(771, 16823, F7, 14) (dual of [16823, 16752, 15]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 29 | Linear OA(795, 823559, F7, 14) (dual of [823559, 823464, 15]-code) | [i] | ||
| 30 | Linear OA(766, 16823, F7, 13) (dual of [16823, 16757, 14]-code) | [i] | ||
| 31 | Linear OA(788, 823559, F7, 13) (dual of [823559, 823471, 14]-code) | [i] | ||
| 32 | Linear OA(744, 56, F7, 31) (dual of [56, 12, 32]-code) | [i] | Construction X with Cyclic Codes | |
| 33 | Linear OA(748, 56, F7, 37) (dual of [56, 8, 38]-code) | [i] | ||
| 34 | Linear OA(743, 56, F7, 30) (dual of [56, 13, 31]-code) | [i] | ||
| 35 | Linear OA(742, 65, F7, 22) (dual of [65, 23, 23]-code) | [i] | ||
| 36 | Linear OA(741, 65, F7, 21) (dual of [65, 24, 22]-code) | [i] | ||
| 37 | Linear OA(729, 58, F7, 16) (dual of [58, 29, 17]-code) | [i] | ||
| 38 | Linear OA(749, 57, F7, 38) (dual of [57, 8, 39]-code) | [i] | Construction XX with Cyclic Codes | |
| 39 | Linear OA(744, 57, F7, 31) (dual of [57, 13, 32]-code) | [i] | ||
| 40 | Linear OA(743, 67, F7, 22) (dual of [67, 24, 23]-code) | [i] | ||
| 41 | Linear OA(732, 60, F7, 18) (dual of [60, 28, 19]-code) | [i] | ||
| 42 | Linear OA(735, 63, F7, 19) (dual of [63, 28, 20]-code) | [i] | ||
| 43 | Linear OA(739, 67, F7, 20) (dual of [67, 28, 21]-code) | [i] | ||
| 44 | Linear OA(737, 64, F7, 20) (dual of [64, 27, 21]-code) | [i] | ||
| 45 | Linear OA(741, 68, F7, 21) (dual of [68, 27, 22]-code) | [i] | ||
| 46 | Linear OA(743, 63, F7, 26) (dual of [63, 20, 27]-code) | [i] | ||
| 47 | Linear OA(742, 61, F7, 26) (dual of [61, 19, 27]-code) | [i] | ||
| 48 | Linear OA(745, 64, F7, 27) (dual of [64, 19, 28]-code) | [i] | ||
| 49 | Linear OA(745, 74, F7, 23) (dual of [74, 29, 24]-code) | [i] | ||
| 50 | Linear OA(747, 76, F7, 24) (dual of [76, 29, 25]-code) | [i] | ||
| 51 | Linear OA(744, 72, F7, 23) (dual of [72, 28, 24]-code) | [i] | ||
| 52 | Linear OA(746, 74, F7, 24) (dual of [74, 28, 25]-code) | [i] | ||
| 53 | Linear OA(741, 67, F7, 22) (dual of [67, 26, 23]-code) | [i] | ||
| 54 | Linear OA(752, 72, F7, 30) (dual of [72, 20, 31]-code) | [i] | ||
| 55 | Linear OA(751, 70, F7, 30) (dual of [70, 19, 31]-code) | [i] | ||
| 56 | Linear OA(749, 67, F7, 29) (dual of [67, 18, 30]-code) | [i] | ||
| 57 | Linear OA(749, 66, F7, 30) (dual of [66, 17, 31]-code) | [i] | ||
| 58 | Linear OA(747, 64, F7, 29) (dual of [64, 17, 30]-code) | [i] | ||
| 59 | Linear OA(747, 64, F7, 29) (dual of [64, 17, 30]-code) | [i] | ||
| 60 | Linear OA(757, 70, F7, 37) (dual of [70, 13, 38]-code) | [i] | ||
| 61 | Linear OA(754, 67, F7, 35) (dual of [67, 13, 36]-code) | [i] | ||
| 62 | Linear OA(756, 67, F7, 37) (dual of [67, 11, 38]-code) | [i] | ||
| 63 | Linear OA(756, 68, F7, 37) (dual of [68, 12, 38]-code) | [i] | ||
| 64 | Linear OA(754, 66, F7, 36) (dual of [66, 12, 37]-code) | [i] | ||
| 65 | Linear OA(752, 64, F7, 35) (dual of [64, 12, 36]-code) | [i] | ||
| 66 | Linear OA(752, 64, F7, 35) (dual of [64, 12, 36]-code) | [i] | ||
| 67 | Linear OA(753, 64, F7, 36) (dual of [64, 11, 37]-code) | [i] | ||
| 68 | Linear OA(753, 63, F7, 37) (dual of [63, 10, 38]-code) | [i] | ||
| 69 | Linear OA(761, 69, F7, 44) (dual of [69, 8, 45]-code) | [i] | ||
| 70 | Linear OA(762, 70, F7, 45) (dual of [70, 8, 46]-code) | [i] | ||
| 71 | Linear OA(759, 67, F7, 43) (dual of [67, 8, 44]-code) | [i] | ||
| 72 | Linear OA(753, 128, F7, 22) (dual of [128, 75, 23]-code) | [i] | ||
| 73 | Linear OA(752, 126, F7, 22) (dual of [126, 74, 23]-code) | [i] | ||
| 74 | Linear OA(756, 130, F7, 23) (dual of [130, 74, 24]-code) | [i] | ||
| 75 | Linear OA(791, 187, F7, 39) (dual of [187, 96, 40]-code) | [i] | ||
| 76 | Linear OA(7106, 187, F7, 46) (dual of [187, 81, 47]-code) | [i] | ||
| 77 | Linear OA(768, 180, F7, 28) (dual of [180, 112, 29]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 78 | Linear OA(737, 57, F7, 24) (dual of [57, 20, 25]-code) | [i] | ||
| 79 | Linear OA(731, 57, F7, 18) (dual of [57, 26, 19]-code) | [i] | ||
| 80 | Linear OA(729, 57, F7, 17) (dual of [57, 28, 18]-code) | [i] | ||
| 81 | Linear OA(769, 181, F7, 29) (dual of [181, 112, 30]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 82 | Linear OA(764, 77, F7, 40) (dual of [77, 13, 41]-code) | [i] | ||
| 83 | Linear OA(763, 76, F7, 40) (dual of [76, 13, 41]-code) | [i] | ||
| 84 | Linear OA(739, 58, F7, 25) (dual of [58, 19, 26]-code) | [i] | ||