Information on Result #805776
Linear OOA(251, 136, F2, 2, 13) (dual of [(136, 2), 221, 14]-NRT-code), using OOA 2-folding based on linear OA(251, 272, F2, 13) (dual of [272, 221, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 273, F2, 13) (dual of [273, 222, 14]-code), using
- construction XX applied to C1 = C([253,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([253,10]) [i] based on
- linear OA(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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)
- construction XX applied to C1 = C([253,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([253,10]) [i] based on
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 OOA(251, 122, F2, 3, 13) (dual of [(122, 3), 315, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(251, 122, F2, 4, 13) (dual of [(122, 4), 437, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(251, 122, F2, 5, 13) (dual of [(122, 5), 559, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(251, 122, F2, 6, 13) (dual of [(122, 6), 681, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(251, 122, F2, 7, 13) (dual of [(122, 7), 803, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(251, 122, F2, 8, 13) (dual of [(122, 8), 925, 14]-NRT-code) | [i] | ||
| 7 | Digital (38, 51, 122)-net over F2 | [i] | ||