Information on Result #609774
Linear OA(164, 257, F16, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)), using ovoid in PG(3, 16)
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(1623, 4354, F16, 7) (dual of [4354, 4331, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(1630, 131331, F16, 7) (dual of [131331, 131301, 8]-code) | [i] | ||
| 3 | Linear OA(1635, 1048834, F16, 7) (dual of [1048834, 1048799, 8]-code) | [i] | ||
| 4 | Linear OA(1630, 1048833, F16, 6) (dual of [1048833, 1048803, 7]-code) | [i] | ||
| 5 | Linear OA(1623, 4356, F16, 7) (dual of [4356, 4333, 8]-code) | [i] | ||
| 6 | Linear OA(1630, 131333, F16, 7) (dual of [131333, 131303, 8]-code) | [i] | ||
| 7 | Linear OA(1635, 1048838, F16, 7) (dual of [1048838, 1048803, 8]-code) | [i] | ||
| 8 | Linear OA(1630, 1048838, F16, 6) (dual of [1048838, 1048808, 7]-code) | [i] | ||
| 9 | Linear OA(16130, 134, F16, 115) (dual of [134, 4, 116]-code) | [i] | Dual Code (with Bound on d by Construction Y1) | |
| 10 | Linear OA(169, 1188882, F16, 3) (dual of [1188882, 1188873, 4]-code or 1188882-cap in PG(8,16)) | [i] | Product of Two Projective Caps and (Hyper)oval | |
| 11 | Linear OA(169, 1188882, F16, 3) (dual of [1188882, 1188873, 4]-code or 1188882-cap in PG(8,16)) | [i] | ||
| 12 | Linear OA(16125, 1048601, F16, 25) (dual of [1048601, 1048476, 26]-code) | [i] | Construction X with Cyclic Codes | |
| 13 | Linear OA(16115, 1048601, F16, 23) (dual of [1048601, 1048486, 24]-code) | [i] | ||
| 14 | Linear OA(16105, 1048601, F16, 21) (dual of [1048601, 1048496, 22]-code) | [i] | ||
| 15 | Linear OA(1695, 1048601, F16, 19) (dual of [1048601, 1048506, 20]-code) | [i] | ||
| 16 | Linear OA(1685, 1048601, F16, 17) (dual of [1048601, 1048516, 18]-code) | [i] | ||
| 17 | Linear OA(1675, 1048601, F16, 15) (dual of [1048601, 1048526, 16]-code) | [i] | ||
| 18 | Linear OA(1665, 1048601, F16, 13) (dual of [1048601, 1048536, 14]-code) | [i] | ||
| 19 | Linear OA(1655, 1048601, F16, 11) (dual of [1048601, 1048546, 12]-code) | [i] | ||
| 20 | Linear OA(1645, 1048601, F16, 9) (dual of [1048601, 1048556, 10]-code) | [i] | ||
| 21 | Linear OA(16130, 1048600, F16, 27) (dual of [1048600, 1048470, 28]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 22 | Linear OA(16125, 1048600, F16, 26) (dual of [1048600, 1048475, 27]-code) | [i] | ||
| 23 | Linear OA(16120, 1048600, F16, 25) (dual of [1048600, 1048480, 26]-code) | [i] | ||
| 24 | Linear OA(16115, 1048600, F16, 24) (dual of [1048600, 1048485, 25]-code) | [i] | ||
| 25 | Linear OA(16110, 1048600, F16, 23) (dual of [1048600, 1048490, 24]-code) | [i] | ||
| 26 | Linear OA(16105, 1048600, F16, 22) (dual of [1048600, 1048495, 23]-code) | [i] | ||
| 27 | Linear OA(16100, 1048600, F16, 21) (dual of [1048600, 1048500, 22]-code) | [i] | ||
| 28 | Linear OA(1680, 1048600, F16, 16) (dual of [1048600, 1048520, 17]-code) | [i] | ||
| 29 | Linear OA(1670, 1048600, F16, 14) (dual of [1048600, 1048530, 15]-code) | [i] | ||
| 30 | Linear OA(1660, 1048600, F16, 12) (dual of [1048600, 1048540, 13]-code) | [i] | ||
| 31 | Linear OA(1650, 1048600, F16, 10) (dual of [1048600, 1048550, 11]-code) | [i] | ||
| 32 | Linear OA(1640, 1048600, F16, 8) (dual of [1048600, 1048560, 9]-code) | [i] | ||
| 33 | Linear OA(16121, 65556, F16, 31) (dual of [65556, 65435, 32]-code) | [i] | ||
| 34 | Linear OA(16117, 65556, F16, 30) (dual of [65556, 65439, 31]-code) | [i] | ||
| 35 | Linear OA(16113, 65556, F16, 29) (dual of [65556, 65443, 30]-code) | [i] | ||
| 36 | Linear OA(16109, 65556, F16, 28) (dual of [65556, 65447, 29]-code) | [i] | ||
| 37 | Linear OA(16105, 65556, F16, 27) (dual of [65556, 65451, 28]-code) | [i] | ||
| 38 | Linear OA(16101, 65556, F16, 26) (dual of [65556, 65455, 27]-code) | [i] | ||
| 39 | Linear OA(1697, 65556, F16, 25) (dual of [65556, 65459, 26]-code) | [i] | ||
| 40 | Linear OA(1693, 65556, F16, 24) (dual of [65556, 65463, 25]-code) | [i] | ||
| 41 | Linear OA(1689, 65556, F16, 23) (dual of [65556, 65467, 24]-code) | [i] | ||
| 42 | Linear OA(1685, 65556, F16, 22) (dual of [65556, 65471, 23]-code) | [i] | ||
| 43 | Linear OA(1681, 65556, F16, 21) (dual of [65556, 65475, 22]-code) | [i] | ||
| 44 | Linear OA(16126, 1048602, F16, 26) (dual of [1048602, 1048476, 27]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 45 | Linear OA(16121, 1048602, F16, 25) (dual of [1048602, 1048481, 26]-code) | [i] | ||
| 46 | Linear OA(16116, 1048602, F16, 24) (dual of [1048602, 1048486, 25]-code) | [i] | ||
| 47 | Linear OA(16111, 1048602, F16, 23) (dual of [1048602, 1048491, 24]-code) | [i] | ||
| 48 | Linear OA(16106, 1048602, F16, 22) (dual of [1048602, 1048496, 23]-code) | [i] | ||
| 49 | Linear OA(16102, 1048603, F16, 21) (dual of [1048603, 1048501, 22]-code) | [i] | ||
| 50 | Linear OA(1681, 1048602, F16, 16) (dual of [1048602, 1048521, 17]-code) | [i] | ||
| 51 | Linear OA(1671, 1048602, F16, 14) (dual of [1048602, 1048531, 15]-code) | [i] | ||
| 52 | Linear OA(1661, 1048602, F16, 12) (dual of [1048602, 1048541, 13]-code) | [i] | ||
| 53 | Linear OA(1651, 1048602, F16, 10) (dual of [1048602, 1048551, 11]-code) | [i] | ||
| 54 | Linear OA(1641, 1048602, F16, 8) (dual of [1048602, 1048561, 9]-code) | [i] | ||
| 55 | Linear OOA(164, 257, F16, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code) | [i] | OAs with Strength 3, b ≠ 2, and m > 3 Are Always Embeddable | |