Information on Result #2223991
Linear OA(2142, 272, F2, 40) (dual of [272, 130, 41]-code), using 1 times truncation based on linear OA(2143, 273, F2, 41) (dual of [273, 130, 42]-code), using
- construction XX applied to C1 = C([253,36]), C2 = C([0,38]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([253,38]) [i] 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(2133, 255, F2, 39) (dual of [255, 122, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [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(2125, 255, F2, 37) (dual of [255, 130, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- 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
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (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(2151, 283, F2, 40) (dual of [283, 132, 41]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(2142, 136, F2, 2, 40) (dual of [(136, 2), 130, 41]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2142, 90, F2, 3, 40) (dual of [(90, 3), 128, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2142, 68, F2, 4, 40) (dual of [(68, 4), 130, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2142, 54, F2, 5, 40) (dual of [(54, 5), 128, 41]-NRT-code) | [i] | ||