Information on Result #2226284
Linear OA(2192, 558, F2, 42) (dual of [558, 366, 43]-code), using 1 times truncation based on linear OA(2193, 559, F2, 43) (dual of [559, 366, 44]-code), using
- construction XX applied to C1 = C([507,34]), C2 = C([0,38]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([507,38]) [i] based on
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-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(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)) (see above)
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(2200, 568, F2, 42) (dual of [568, 368, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(2192, 279, F2, 2, 42) (dual of [(279, 2), 366, 43]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2192, 186, F2, 3, 42) (dual of [(186, 3), 366, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(2192, 139, F2, 4, 42) (dual of [(139, 4), 364, 43]-NRT-code) | [i] | ||