Information on Result #2226084
Linear OA(2186, 536, F2, 42) (dual of [536, 350, 43]-code), using 1 times truncation based on linear OA(2187, 537, F2, 43) (dual of [537, 350, 44]-code), using
- construction XX applied to C1 = C([507,36]), C2 = C([0,38]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([507,38]) [i] based on
- linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [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(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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(2186, 268, F2, 2, 42) (dual of [(268, 2), 350, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2186, 134, F2, 4, 42) (dual of [(134, 4), 350, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(2186, 107, F2, 5, 42) (dual of [(107, 5), 349, 43]-NRT-code) | [i] | ||