Information on Result #701942
Linear OA(2143, 274, F2, 40) (dual of [274, 131, 41]-code), using construction XX applied to C1 = C([253,36]), C2 = C([1,38]), C3 = C1 + C2 = C([1,36]), and C∩ = C1 ∩ C2 = C([253,38]) based on
- linear OA(2133, 255, F2, 39) (dual of [255, 122, 40]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2132, 255, F2, 38) (dual of [255, 123, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [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 = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2124, 255, F2, 36) (dual of [255, 131, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(2148, 279, F2, 40) (dual of [279, 131, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2144, 275, F2, 41) (dual of [275, 131, 42]-code) | [i] | Adding a Parity Check Bit | |
| 3 | Linear OA(2149, 281, F2, 40) (dual of [281, 132, 41]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OA(2152, 285, F2, 40) (dual of [285, 133, 41]-code) | [i] | ||
| 5 | Linear OOA(2143, 137, F2, 2, 40) (dual of [(137, 2), 131, 41]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2143, 91, F2, 3, 40) (dual of [(91, 3), 130, 41]-NRT-code) | [i] | ||