Information on Result #701960
Linear OA(2155, 278, F2, 44) (dual of [278, 123, 45]-code), using construction XX applied to C1 = C([213,254]), C2 = C([217,2]), C3 = C1 + C2 = C([217,254]), and C∩ = C1 ∩ C2 = C([213,2]) based on
- linear OA(2140, 255, F2, 42) (dual of [255, 115, 43]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−42,−41,…,−1}, and designed minimum distance d ≥ |I|+1 = 43 [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 = {−38,−37,…,2}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−42,−41,…,2}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2132, 255, F2, 38) (dual of [255, 123, 39]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,−1}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(25, 13, F2, 3) (dual of [13, 8, 4]-code or 13-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on 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 OA(2156, 279, F2, 45) (dual of [279, 123, 46]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2155, 139, F2, 2, 44) (dual of [(139, 2), 123, 45]-NRT-code) | [i] | OOA Folding | |