Information on Result #625107
Linear OA(1660, 64, F16, 55) (dual of [64, 4, 56]-code), using algebraic-geometric code AG(F,8P) 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(16124, 128, F16, 111) (dual of [128, 4, 112]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(1664, 68, F16, 56) (dual of [68, 4, 57]-code) | [i] | Juxtaposition | |
| 3 | Linear OA(1665, 69, F16, 57) (dual of [69, 4, 58]-code) | [i] | ||
| 4 | Linear OA(1666, 70, F16, 58) (dual of [70, 4, 59]-code) | [i] | ||
| 5 | Linear OA(1667, 71, F16, 59) (dual of [71, 4, 60]-code) | [i] | ||
| 6 | Linear OA(1668, 72, F16, 60) (dual of [72, 4, 61]-code) | [i] | ||
| 7 | Linear OA(1669, 73, F16, 61) (dual of [73, 4, 62]-code) | [i] | ||
| 8 | Linear OA(1670, 74, F16, 62) (dual of [74, 4, 63]-code) | [i] | ||
| 9 | Linear OA(1671, 75, F16, 63) (dual of [75, 4, 64]-code) | [i] | ||
| 10 | Linear OA(1672, 76, F16, 64) (dual of [76, 4, 65]-code) | [i] | ||
| 11 | Linear OA(1673, 77, F16, 65) (dual of [77, 4, 66]-code) | [i] | ||
| 12 | Linear OA(1674, 78, F16, 66) (dual of [78, 4, 67]-code) | [i] | ||
| 13 | Linear OA(1675, 79, F16, 67) (dual of [79, 4, 68]-code) | [i] | ||
| 14 | Linear OA(1676, 80, F16, 68) (dual of [80, 4, 69]-code) | [i] | ||
| 15 | Linear OA(1677, 81, F16, 69) (dual of [81, 4, 70]-code) | [i] | ||
| 16 | Linear OA(1679, 83, F16, 70) (dual of [83, 4, 71]-code) | [i] | ||
| 17 | Linear OA(1680, 84, F16, 71) (dual of [84, 4, 72]-code) | [i] | ||
| 18 | Linear OA(1681, 85, F16, 72) (dual of [85, 4, 73]-code) | [i] | ||
| 19 | Linear OA(1682, 86, F16, 73) (dual of [86, 4, 74]-code) | [i] | ||
| 20 | Linear OA(1683, 87, F16, 74) (dual of [87, 4, 75]-code) | [i] | ||
| 21 | Linear OA(1684, 88, F16, 75) (dual of [88, 4, 76]-code) | [i] | ||
| 22 | Linear OA(1686, 90, F16, 76) (dual of [90, 4, 77]-code) | [i] | ||
| 23 | Linear OA(1687, 91, F16, 77) (dual of [91, 4, 78]-code) | [i] | ||
| 24 | Linear OA(1688, 92, F16, 78) (dual of [92, 4, 79]-code) | [i] | ||
| 25 | Linear OA(1689, 93, F16, 79) (dual of [93, 4, 80]-code) | [i] | ||
| 26 | Linear OA(1690, 94, F16, 80) (dual of [94, 4, 81]-code) | [i] | ||
| 27 | Linear OA(1691, 95, F16, 81) (dual of [95, 4, 82]-code) | [i] | ||
| 28 | Linear OA(1692, 96, F16, 82) (dual of [96, 4, 83]-code) | [i] | ||
| 29 | Linear OA(1693, 97, F16, 83) (dual of [97, 4, 84]-code) | [i] | ||
| 30 | Linear OA(1695, 99, F16, 84) (dual of [99, 4, 85]-code) | [i] | ||
| 31 | Linear OA(1696, 100, F16, 85) (dual of [100, 4, 86]-code) | [i] | ||
| 32 | Linear OA(1697, 101, F16, 86) (dual of [101, 4, 87]-code) | [i] | ||
| 33 | Linear OA(1698, 102, F16, 87) (dual of [102, 4, 88]-code) | [i] | ||
| 34 | Linear OA(16102, 106, F16, 90) (dual of [106, 4, 91]-code) | [i] | ||
| 35 | Linear OA(16103, 107, F16, 91) (dual of [107, 4, 92]-code) | [i] | ||
| 36 | Linear OA(16104, 108, F16, 92) (dual of [108, 4, 93]-code) | [i] | ||
| 37 | Linear OA(16105, 109, F16, 93) (dual of [109, 4, 94]-code) | [i] | ||
| 38 | Linear OA(1663, 67, F16, 58) (dual of [67, 4, 59]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 39 | Linear OA(1660, 65, F16, 55) (dual of [65, 5, 56]-code) | [i] | ✔ | |
| 40 | Linear OA(1665, 69, F16, 59) (dual of [69, 4, 60]-code) | [i] | ✔ | |
| 41 | Linear OA(1661, 67, F16, 55) (dual of [67, 6, 56]-code) | [i] | ✔ | |
| 42 | Linear OA(1670, 74, F16, 63) (dual of [74, 4, 64]-code) | [i] | ✔ | |
| 43 | Linear OA(1663, 70, F16, 55) (dual of [70, 7, 56]-code) | [i] | ✔ | |
| 44 | Linear OA(1664, 72, F16, 55) (dual of [72, 8, 56]-code) | [i] | ✔ | |
| 45 | Linear OA(1665, 74, F16, 55) (dual of [74, 9, 56]-code) | [i] | ✔ | |
| 46 | Linear OA(1666, 76, F16, 55) (dual of [76, 10, 56]-code) | [i] | ✔ | |
| 47 | Linear OA(1667, 78, F16, 55) (dual of [78, 11, 56]-code) | [i] | ✔ | |
| 48 | Linear OA(1668, 80, F16, 55) (dual of [80, 12, 56]-code) | [i] | ✔ | |
| 49 | Linear OA(1670, 83, F16, 55) (dual of [83, 13, 56]-code) | [i] | ✔ | |
| 50 | Linear OA(1671, 85, F16, 55) (dual of [85, 14, 56]-code) | [i] | ✔ | |
| 51 | Linear OA(1672, 87, F16, 55) (dual of [87, 15, 56]-code) | [i] | ✔ | |
| 52 | Linear OA(1674, 90, F16, 55) (dual of [90, 16, 56]-code) | [i] | ✔ | |
| 53 | Linear OA(1675, 92, F16, 55) (dual of [92, 17, 56]-code) | [i] | ✔ | |
| 54 | Linear OA(1676, 94, F16, 55) (dual of [94, 18, 56]-code) | [i] | ✔ | |
| 55 | Linear OA(1677, 96, F16, 55) (dual of [96, 19, 56]-code) | [i] | ✔ | |
| 56 | Linear OA(1679, 99, F16, 55) (dual of [99, 20, 56]-code) | [i] | ✔ | |
| 57 | Linear OA(1680, 101, F16, 55) (dual of [101, 21, 56]-code) | [i] | ✔ | |
| 58 | Linear OA(1682, 104, F16, 55) (dual of [104, 22, 56]-code) | [i] | ✔ | |
| 59 | Linear OA(1683, 106, F16, 55) (dual of [106, 23, 56]-code) | [i] | ✔ | |
| 60 | Linear OA(1684, 108, F16, 55) (dual of [108, 24, 56]-code) | [i] | ✔ | |
| 61 | Linear OA(1686, 111, F16, 55) (dual of [111, 25, 56]-code) | [i] | ✔ | |
| 62 | Linear OA(1687, 113, F16, 55) (dual of [113, 26, 56]-code) | [i] | ✔ | |
| 63 | Linear OA(1689, 116, F16, 55) (dual of [116, 27, 56]-code) | [i] | ✔ | |
| 64 | Linear OA(1690, 118, F16, 55) (dual of [118, 28, 56]-code) | [i] | ✔ | |
| 65 | Linear OA(1691, 120, F16, 55) (dual of [120, 29, 56]-code) | [i] | ✔ | |
| 66 | Linear OA(1692, 122, F16, 55) (dual of [122, 30, 56]-code) | [i] | ✔ | |
| 67 | Linear OA(1693, 124, F16, 55) (dual of [124, 31, 56]-code) | [i] | ✔ | |
| 68 | Linear OA(1669, 82, F16, 55) (dual of [82, 13, 56]-code) | [i] | ✔ | Construction XX with a Chain of Algebraic-Geometric Codes |
| 69 | Linear OA(1673, 89, F16, 55) (dual of [89, 16, 56]-code) | [i] | ✔ | |
| 70 | Linear OOA(1660, 32, F16, 2, 55) (dual of [(32, 2), 4, 56]-NRT-code) | [i] | OOA Folding | |