Information on Result #701988
Linear OA(2159, 274, F2, 46) (dual of [274, 115, 47]-code), using construction XX applied to C1 = C([253,42]), C2 = C([1,44]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([253,44]) based on
- 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 = {−2,−1,…,42}, and designed minimum distance d ≥ |I|+1 = 46 [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(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 = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [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(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
- 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 (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(2164, 279, F2, 46) (dual of [279, 115, 47]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2165, 280, F2, 46) (dual of [280, 115, 47]-code) | [i] | ||
| 3 | Linear OA(2160, 275, F2, 47) (dual of [275, 115, 48]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OA(2165, 281, F2, 46) (dual of [281, 116, 47]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(2159, 137, F2, 2, 46) (dual of [(137, 2), 115, 47]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2159, 91, F2, 3, 46) (dual of [(91, 3), 114, 47]-NRT-code) | [i] | ||