Information on Result #2175078
Linear OA(2160, 303, F2, 41) (dual of [303, 143, 42]-code), using adding a parity check bit based on linear OA(2159, 302, F2, 40) (dual of [302, 143, 41]-code), using
- construction XX applied to C1 = C([219,254]), C2 = C([227,4]), C3 = C1 + C2 = C([227,254]), and C∩ = C1 ∩ C2 = C([219,4]) [i] based on
- linear OA(2124, 255, F2, 36) (dual of [255, 131, 37]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−36,−35,…,−1}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2125, 255, F2, 33) (dual of [255, 130, 34]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−28,−27,…,4}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2141, 255, F2, 41) (dual of [255, 114, 42]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−36,−35,…,4}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2108, 255, F2, 28) (dual of [255, 147, 29]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−28,−27,…,−1}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- extended Golay code Ge(2) [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
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(2160, 303, F2, 40) (dual of [303, 143, 41]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2161, 304, F2, 41) (dual of [304, 143, 42]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2162, 305, F2, 41) (dual of [305, 143, 42]-code) | [i] | ||
| 4 | Linear OOA(2160, 151, F2, 2, 41) (dual of [(151, 2), 142, 42]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2160, 101, F2, 3, 41) (dual of [(101, 3), 143, 42]-NRT-code) | [i] | ||