Information on Result #617445
Linear OA(2737, 531441, F27, 10) (dual of [531441, 531404, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10
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(2742, 531469, F27, 10) (dual of [531469, 531427, 11]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2743, 531479, F27, 10) (dual of [531479, 531436, 11]-code) | [i] | ||
| 3 | Linear OA(2744, 532144, F27, 10) (dual of [532144, 532100, 11]-code) | [i] | ||
| 4 | Linear OA(2745, 531450, F27, 10) (dual of [531450, 531405, 11]-code) | [i] | Generalized (u, u+v)-Construction | |
| 5 | Linear OOA(2737, 399807, F27, 2, 10) (dual of [(399807, 2), 799577, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (27, 37, 399807)-net over F27 | [i] | ||
| 7 | Linear OA(2744, 531449, F27, 10) (dual of [531449, 531405, 11]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 8 | Linear OA(2745, 531497, F27, 10) (dual of [531497, 531452, 11]-code) | [i] | ||
| 9 | Linear OA(2741, 531445, F27, 11) (dual of [531445, 531404, 12]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 10 | Linear OA(2737, 531445, F27, 10) (dual of [531445, 531408, 11]-code) | [i] | ✔ | |
| 11 | Linear OA(2746, 531450, F27, 12) (dual of [531450, 531404, 13]-code) | [i] | ✔ | |
| 12 | Linear OA(2738, 531450, F27, 10) (dual of [531450, 531412, 11]-code) | [i] | ✔ | |
| 13 | Linear OA(2751, 531455, F27, 13) (dual of [531455, 531404, 14]-code) | [i] | ✔ | |
| 14 | Linear OA(2739, 531455, F27, 10) (dual of [531455, 531416, 11]-code) | [i] | ✔ | |
| 15 | Linear OA(2756, 531460, F27, 14) (dual of [531460, 531404, 15]-code) | [i] | ✔ | |
| 16 | Linear OA(2740, 531460, F27, 10) (dual of [531460, 531420, 11]-code) | [i] | ✔ | |
| 17 | Linear OA(2761, 531465, F27, 15) (dual of [531465, 531404, 16]-code) | [i] | ✔ | |
| 18 | Linear OA(2741, 531465, F27, 10) (dual of [531465, 531424, 11]-code) | [i] | ✔ | |
| 19 | Linear OA(2766, 531469, F27, 16) (dual of [531469, 531403, 17]-code) | [i] | ✔ | |
| 20 | Linear OA(2767, 531471, F27, 16) (dual of [531471, 531404, 17]-code) | [i] | ✔ | |
| 21 | Linear OA(2772, 531476, F27, 17) (dual of [531476, 531404, 18]-code) | [i] | ✔ | |
| 22 | Linear OA(2777, 531479, F27, 18) (dual of [531479, 531402, 19]-code) | [i] | ✔ | |
| 23 | Linear OA(2778, 531482, F27, 18) (dual of [531482, 531404, 19]-code) | [i] | ✔ | |
| 24 | Linear OA(2783, 531487, F27, 19) (dual of [531487, 531404, 20]-code) | [i] | ✔ | |
| 25 | Linear OA(2788, 531489, F27, 20) (dual of [531489, 531401, 21]-code) | [i] | ✔ | |
| 26 | Linear OA(2789, 531493, F27, 20) (dual of [531493, 531404, 21]-code) | [i] | ✔ | |
| 27 | Linear OA(2750, 531455, F27, 12) (dual of [531455, 531405, 13]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |