Information on Result #2175099
Linear OA(2173, 288, F2, 49) (dual of [288, 115, 50]-code), using adding a parity check bit based on linear OA(2172, 287, F2, 48) (dual of [287, 115, 49]-code), using
- construction XX applied to C1 = C([251,42]), C2 = C([1,44]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([251,44]) [i] based on
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2148, 255, F2, 44) (dual of [255, 107, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2165, 255, F2, 49) (dual of [255, 90, 50]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2140, 255, F2, 42) (dual of [255, 115, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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, 9, F2, 1) (dual of [9, 8, 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 OA(2173, 288, F2, 48) (dual of [288, 115, 49]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2174, 289, F2, 49) (dual of [289, 115, 50]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2175, 290, F2, 49) (dual of [290, 115, 50]-code) | [i] | ||
| 4 | Linear OOA(2173, 144, F2, 2, 49) (dual of [(144, 2), 115, 50]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2173, 96, F2, 3, 49) (dual of [(96, 3), 115, 50]-NRT-code) | [i] | ||