Information on Result #2258805
Linear OA(294, 285, F2, 22) (dual of [285, 191, 23]-code), using 2 times code embedding in larger space based on linear OA(292, 283, F2, 22) (dual of [283, 191, 23]-code), using
- construction XX applied to C1 = C([251,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([251,18]) [i] based on
- linear OA(281, 255, F2, 21) (dual of [255, 174, 22]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(268, 255, F2, 18) (dual of [255, 187, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(264, 255, F2, 16) (dual of [255, 191, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(26, 23, F2, 3) (dual of [23, 17, 4]-code or 23-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 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 OOA(294, 95, F2, 3, 22) (dual of [(95, 3), 191, 23]-NRT-code) | [i] | OOA Folding | |