Information on Result #617516
Linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 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(2769, 531469, F27, 16) (dual of [531469, 531400, 17]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2770, 531479, F27, 16) (dual of [531479, 531409, 17]-code) | [i] | ||
| 3 | Linear OA(2771, 531489, F27, 16) (dual of [531489, 531418, 17]-code) | [i] | ||
| 4 | Linear OA(2772, 531493, F27, 16) (dual of [531493, 531421, 17]-code) | [i] | ||
| 5 | Linear OA(2773, 531505, F27, 16) (dual of [531505, 531432, 17]-code) | [i] | ||
| 6 | Linear OA(2774, 531509, F27, 16) (dual of [531509, 531435, 17]-code) | [i] | ||
| 7 | Linear OA(2775, 531624, F27, 16) (dual of [531624, 531549, 17]-code) | [i] | ||
| 8 | Linear OA(2775, 531456, F27, 16) (dual of [531456, 531381, 17]-code) | [i] | Generalized (u, u+v)-Construction | |
| 9 | Linear OOA(2761, 316878, F27, 2, 16) (dual of [(316878, 2), 633695, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 10 | Digital (45, 61, 316878)-net over F27 | [i] | ||
| 11 | Linear OA(2772, 531453, F27, 16) (dual of [531453, 531381, 17]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 12 | Linear OA(2773, 531455, F27, 16) (dual of [531455, 531382, 17]-code) | [i] | ||
| 13 | Linear OA(2774, 531497, F27, 16) (dual of [531497, 531423, 17]-code) | [i] | ||
| 14 | Linear OA(2775, 531507, F27, 16) (dual of [531507, 531432, 17]-code) | [i] | ||
| 15 | Linear OA(2765, 531445, F27, 17) (dual of [531445, 531380, 18]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 16 | Linear OA(2761, 531445, F27, 16) (dual of [531445, 531384, 17]-code) | [i] | ✔ | |
| 17 | Linear OA(2770, 531450, F27, 18) (dual of [531450, 531380, 19]-code) | [i] | ✔ | |
| 18 | Linear OA(2762, 531450, F27, 16) (dual of [531450, 531388, 17]-code) | [i] | ✔ | |
| 19 | Linear OA(2775, 531455, F27, 19) (dual of [531455, 531380, 20]-code) | [i] | ✔ | |
| 20 | Linear OA(2763, 531455, F27, 16) (dual of [531455, 531392, 17]-code) | [i] | ✔ | |
| 21 | Linear OA(2780, 531460, F27, 20) (dual of [531460, 531380, 21]-code) | [i] | ✔ | |
| 22 | Linear OA(2764, 531460, F27, 16) (dual of [531460, 531396, 17]-code) | [i] | ✔ | |
| 23 | Linear OA(2785, 531465, F27, 21) (dual of [531465, 531380, 22]-code) | [i] | ✔ | |
| 24 | Linear OA(2765, 531465, F27, 16) (dual of [531465, 531400, 17]-code) | [i] | ✔ | |
| 25 | Linear OA(2790, 531469, F27, 22) (dual of [531469, 531379, 23]-code) | [i] | ✔ | |
| 26 | Linear OA(2791, 531471, F27, 22) (dual of [531471, 531380, 23]-code) | [i] | ✔ | |
| 27 | Linear OA(2766, 531469, F27, 16) (dual of [531469, 531403, 17]-code) | [i] | ✔ | |
| 28 | Linear OA(2767, 531471, F27, 16) (dual of [531471, 531404, 17]-code) | [i] | ✔ | |
| 29 | Linear OA(2796, 531476, F27, 23) (dual of [531476, 531380, 24]-code) | [i] | ✔ | |
| 30 | Linear OA(2768, 531476, F27, 16) (dual of [531476, 531408, 17]-code) | [i] | ✔ | |
| 31 | Linear OA(27101, 531479, F27, 24) (dual of [531479, 531378, 25]-code) | [i] | ✔ | |
| 32 | Linear OA(27102, 531482, F27, 24) (dual of [531482, 531380, 25]-code) | [i] | ✔ | |
| 33 | Linear OA(2769, 531479, F27, 16) (dual of [531479, 531410, 17]-code) | [i] | ✔ | |
| 34 | Linear OA(2770, 531482, F27, 16) (dual of [531482, 531412, 17]-code) | [i] | ✔ | |
| 35 | Linear OA(27107, 531487, F27, 25) (dual of [531487, 531380, 26]-code) | [i] | ✔ | |
| 36 | Linear OOA(2761, 66430, F27, 16, 16) (dual of [(66430, 16), 1062819, 17]-NRT-code) | [i] | OA Folding and Stacking | |