Information on Result #976223
Linear OOA(780, 274520, F7, 3, 13) (dual of [(274520, 3), 823480, 14]-NRT-code), using OOA 3-folding based on linear OA(780, 823560, F7, 13) (dual of [823560, 823480, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(779, 823559, F7, 13) (dual of [823559, 823480, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
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 OOA(787, 274533, F7, 3, 13) (dual of [(274533, 3), 823512, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |