Information on Result #617384
Linear OA(276, 30, F27, 5) (dual of [30, 24, 6]-code), using construction X applied to C([0,2]) ⊂ C([1,2]) based on
- linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(274, 28, F27, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,27)), using the narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [1,2], and minimum distance d ≥ |{1,2}| + |{−3,0}| = 4 (simple Roos-bound) [i]
- linear OA(271, 2, F27, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(27103, 531472, F27, 25) (dual of [531472, 531369, 26]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(2795, 531472, F27, 23) (dual of [531472, 531377, 24]-code) | [i] | ||
| 3 | Linear OA(2787, 531472, F27, 21) (dual of [531472, 531385, 22]-code) | [i] | ||
| 4 | Linear OA(2779, 531472, F27, 19) (dual of [531472, 531393, 20]-code) | [i] | ||
| 5 | Linear OA(2771, 531472, F27, 17) (dual of [531472, 531401, 18]-code) | [i] | ||
| 6 | Linear OA(2763, 531472, F27, 15) (dual of [531472, 531409, 16]-code) | [i] | ||
| 7 | Linear OA(2755, 531472, F27, 13) (dual of [531472, 531417, 14]-code) | [i] | ||
| 8 | Linear OA(27107, 531471, F27, 26) (dual of [531471, 531364, 27]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 9 | Linear OA(2799, 531471, F27, 24) (dual of [531471, 531372, 25]-code) | [i] | ||
| 10 | Linear OA(2791, 531471, F27, 22) (dual of [531471, 531380, 23]-code) | [i] | ||
| 11 | Linear OA(2783, 531471, F27, 20) (dual of [531471, 531388, 21]-code) | [i] | ||
| 12 | Linear OA(2775, 531471, F27, 18) (dual of [531471, 531396, 19]-code) | [i] | ||
| 13 | Linear OA(2767, 531471, F27, 16) (dual of [531471, 531404, 17]-code) | [i] | ||
| 14 | Linear OA(2759, 531471, F27, 14) (dual of [531471, 531412, 15]-code) | [i] | ||
| 15 | Linear OA(2751, 531471, F27, 12) (dual of [531471, 531420, 13]-code) | [i] | ||