Information on Result #2226681
Linear OA(2219, 558, F2, 48) (dual of [558, 339, 49]-code), using 1 times truncation based on linear OA(2220, 559, F2, 49) (dual of [559, 339, 50]-code), using
- construction XX applied to C1 = C([507,40]), C2 = C([0,44]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([507,44]) [i] based on
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [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(2230, 582, F2, 48) (dual of [582, 352, 49]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(2231, 587, F2, 48) (dual of [587, 356, 49]-code) | [i] | ||
| 3 | Linear OA(2232, 593, F2, 48) (dual of [593, 361, 49]-code) | [i] | ||
| 4 | Linear OOA(2219, 279, F2, 2, 48) (dual of [(279, 2), 339, 49]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2219, 186, F2, 3, 48) (dual of [(186, 3), 339, 49]-NRT-code) | [i] | ||
| 6 | Linear OOA(2219, 139, F2, 4, 48) (dual of [(139, 4), 337, 49]-NRT-code) | [i] | ||