Information on Result #625109
Linear OA(1658, 64, F16, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F16 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(16122, 128, F16, 107) (dual of [128, 6, 108]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(16121, 126, F16, 107) (dual of [126, 5, 108]-code) | [i] | ||
| 3 | Linear OA(16120, 124, F16, 107) (dual of [124, 4, 108]-code) | [i] | ||
| 4 | Linear OA(1664, 70, F16, 54) (dual of [70, 6, 55]-code) | [i] | Juxtaposition | |
| 5 | Linear OA(1665, 71, F16, 55) (dual of [71, 6, 56]-code) | [i] | ||
| 6 | Linear OA(1666, 72, F16, 56) (dual of [72, 6, 57]-code) | [i] | ||
| 7 | Linear OA(1667, 73, F16, 57) (dual of [73, 6, 58]-code) | [i] | ||
| 8 | Linear OA(1668, 74, F16, 58) (dual of [74, 6, 59]-code) | [i] | ||
| 9 | Linear OA(1669, 75, F16, 59) (dual of [75, 6, 60]-code) | [i] | ||
| 10 | Linear OA(1670, 76, F16, 60) (dual of [76, 6, 61]-code) | [i] | ||
| 11 | Linear OA(1671, 77, F16, 61) (dual of [77, 6, 62]-code) | [i] | ||
| 12 | Linear OA(1672, 78, F16, 62) (dual of [78, 6, 63]-code) | [i] | ||
| 13 | Linear OA(1673, 79, F16, 63) (dual of [79, 6, 64]-code) | [i] | ||
| 14 | Linear OA(1674, 80, F16, 64) (dual of [80, 6, 65]-code) | [i] | ||
| 15 | Linear OA(1675, 81, F16, 65) (dual of [81, 6, 66]-code) | [i] | ||
| 16 | Linear OA(1677, 83, F16, 66) (dual of [83, 6, 67]-code) | [i] | ||
| 17 | Linear OA(1678, 84, F16, 67) (dual of [84, 6, 68]-code) | [i] | ||
| 18 | Linear OA(1679, 85, F16, 68) (dual of [85, 6, 69]-code) | [i] | ||
| 19 | Linear OA(1680, 86, F16, 69) (dual of [86, 6, 70]-code) | [i] | ||
| 20 | Linear OA(1681, 87, F16, 70) (dual of [87, 6, 71]-code) | [i] | ||
| 21 | Linear OA(1682, 88, F16, 71) (dual of [88, 6, 72]-code) | [i] | ||
| 22 | Linear OA(1684, 90, F16, 72) (dual of [90, 6, 73]-code) | [i] | ||
| 23 | Linear OA(1685, 91, F16, 73) (dual of [91, 6, 74]-code) | [i] | ||
| 24 | Linear OA(1686, 92, F16, 74) (dual of [92, 6, 75]-code) | [i] | ||
| 25 | Linear OA(1687, 93, F16, 75) (dual of [93, 6, 76]-code) | [i] | ||
| 26 | Linear OA(1688, 94, F16, 76) (dual of [94, 6, 77]-code) | [i] | ||
| 27 | Linear OA(1689, 95, F16, 77) (dual of [95, 6, 78]-code) | [i] | ||
| 28 | Linear OA(1690, 96, F16, 78) (dual of [96, 6, 79]-code) | [i] | ||
| 29 | Linear OA(1691, 97, F16, 79) (dual of [97, 6, 80]-code) | [i] | ||
| 30 | Linear OA(1693, 99, F16, 80) (dual of [99, 6, 81]-code) | [i] | ||
| 31 | Linear OA(1694, 100, F16, 81) (dual of [100, 6, 82]-code) | [i] | ||
| 32 | Linear OA(1695, 101, F16, 82) (dual of [101, 6, 83]-code) | [i] | ||
| 33 | Linear OA(1696, 102, F16, 83) (dual of [102, 6, 84]-code) | [i] | ||
| 34 | Linear OA(1698, 104, F16, 84) (dual of [104, 6, 85]-code) | [i] | ||
| 35 | Linear OA(1699, 105, F16, 85) (dual of [105, 6, 86]-code) | [i] | ||
| 36 | Linear OA(16100, 106, F16, 86) (dual of [106, 6, 87]-code) | [i] | ||
| 37 | Linear OA(16101, 107, F16, 87) (dual of [107, 6, 88]-code) | [i] | ||
| 38 | Linear OA(16102, 108, F16, 88) (dual of [108, 6, 89]-code) | [i] | ||
| 39 | Linear OA(16103, 109, F16, 89) (dual of [109, 6, 90]-code) | [i] | ||
| 40 | Linear OA(16129, 135, F16, 112) (dual of [135, 6, 113]-code) | [i] | ||
| 41 | Linear OA(16127, 132, F16, 112) (dual of [132, 5, 113]-code) | [i] | ||
| 42 | Linear OA(1659, 65, F16, 54) (dual of [65, 6, 55]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 43 | Linear OA(1659, 66, F16, 53) (dual of [66, 7, 54]-code) | [i] | ✔ | |
| 44 | Linear OA(1661, 67, F16, 55) (dual of [67, 6, 56]-code) | [i] | ✔ | |
| 45 | Linear OA(1660, 68, F16, 53) (dual of [68, 8, 54]-code) | [i] | ✔ | |
| 46 | Linear OA(1665, 71, F16, 58) (dual of [71, 6, 59]-code) | [i] | ✔ | |
| 47 | Linear OA(1661, 70, F16, 53) (dual of [70, 9, 54]-code) | [i] | ✔ | |
| 48 | Linear OA(1667, 73, F16, 59) (dual of [73, 6, 60]-code) | [i] | ✔ | |
| 49 | Linear OA(1662, 72, F16, 53) (dual of [72, 10, 54]-code) | [i] | ✔ | |
| 50 | Linear OA(1672, 78, F16, 63) (dual of [78, 6, 64]-code) | [i] | ✔ | |
| 51 | Linear OA(1663, 74, F16, 53) (dual of [74, 11, 54]-code) | [i] | ✔ | |
| 52 | Linear OA(1664, 76, F16, 53) (dual of [76, 12, 54]-code) | [i] | ✔ | |
| 53 | Linear OA(1665, 78, F16, 53) (dual of [78, 13, 54]-code) | [i] | ✔ | |
| 54 | Linear OA(1666, 80, F16, 53) (dual of [80, 14, 54]-code) | [i] | ✔ | |
| 55 | Linear OA(1668, 83, F16, 53) (dual of [83, 15, 54]-code) | [i] | ✔ | |
| 56 | Linear OA(1669, 85, F16, 53) (dual of [85, 16, 54]-code) | [i] | ✔ | |
| 57 | Linear OA(1670, 87, F16, 53) (dual of [87, 17, 54]-code) | [i] | ✔ | |
| 58 | Linear OA(1672, 90, F16, 53) (dual of [90, 18, 54]-code) | [i] | ✔ | |
| 59 | Linear OA(1673, 92, F16, 53) (dual of [92, 19, 54]-code) | [i] | ✔ | |
| 60 | Linear OA(1674, 94, F16, 53) (dual of [94, 20, 54]-code) | [i] | ✔ | |
| 61 | Linear OA(1675, 96, F16, 53) (dual of [96, 21, 54]-code) | [i] | ✔ | |
| 62 | Linear OA(1677, 99, F16, 53) (dual of [99, 22, 54]-code) | [i] | ✔ | |
| 63 | Linear OA(1678, 101, F16, 53) (dual of [101, 23, 54]-code) | [i] | ✔ | |
| 64 | Linear OA(1680, 104, F16, 53) (dual of [104, 24, 54]-code) | [i] | ✔ | |
| 65 | Linear OA(1681, 106, F16, 53) (dual of [106, 25, 54]-code) | [i] | ✔ | |
| 66 | Linear OA(1682, 108, F16, 53) (dual of [108, 26, 54]-code) | [i] | ✔ | |
| 67 | Linear OA(1684, 111, F16, 53) (dual of [111, 27, 54]-code) | [i] | ✔ | |
| 68 | Linear OA(1685, 113, F16, 53) (dual of [113, 28, 54]-code) | [i] | ✔ | |
| 69 | Linear OA(1687, 116, F16, 53) (dual of [116, 29, 54]-code) | [i] | ✔ | |
| 70 | Linear OA(1688, 118, F16, 53) (dual of [118, 30, 54]-code) | [i] | ✔ | |
| 71 | Linear OA(1689, 120, F16, 53) (dual of [120, 31, 54]-code) | [i] | ✔ | |
| 72 | Linear OA(1667, 82, F16, 53) (dual of [82, 15, 54]-code) | [i] | ✔ | Construction XX with a Chain of Algebraic-Geometric Codes |
| 73 | Linear OA(1671, 89, F16, 53) (dual of [89, 18, 54]-code) | [i] | ✔ | |
| 74 | Linear OOA(1658, 32, F16, 2, 53) (dual of [(32, 2), 6, 54]-NRT-code) | [i] | OOA Folding | |