Information on Result #806105
Linear OOA(275, 265, F2, 2, 17) (dual of [(265, 2), 455, 18]-NRT-code), using OOA 2-folding based on linear OA(275, 530, F2, 17) (dual of [530, 455, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(275, 531, F2, 17) (dual of [531, 456, 18]-code), using
- construction XX applied to C1 = C([509,12]), C2 = C([0,14]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([509,14]) [i] based on
- linear OA(264, 511, F2, 15) (dual of [511, 447, 16]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(264, 511, F2, 15) (dual of [511, 447, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(255, 511, F2, 13) (dual of [511, 456, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,12]), C2 = C([0,14]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([509,14]) [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(275, 205, F2, 3, 17) (dual of [(205, 3), 540, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(275, 205, F2, 4, 17) (dual of [(205, 4), 745, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(275, 205, F2, 5, 17) (dual of [(205, 5), 950, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(275, 205, F2, 6, 17) (dual of [(205, 6), 1155, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(275, 205, F2, 7, 17) (dual of [(205, 7), 1360, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(275, 205, F2, 8, 17) (dual of [(205, 8), 1565, 18]-NRT-code) | [i] | ||
| 7 | Digital (58, 75, 205)-net over F2 | [i] | ||