Information on Result #806315
Linear OOA(290, 273, F2, 2, 19) (dual of [(273, 2), 456, 20]-NRT-code), using OOA 2-folding based on linear OA(290, 546, F2, 19) (dual of [546, 456, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(290, 547, F2, 19) (dual of [547, 457, 20]-code), using
- adding a parity check bit [i] based on linear OA(289, 546, F2, 18) (dual of [546, 457, 19]-code), using
- construction XX applied to C1 = C([507,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([507,14]) [i] based on
- 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 = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(263, 511, F2, 14) (dual of [511, 448, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(254, 511, F2, 12) (dual of [511, 457, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- 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
- construction XX applied to C1 = C([507,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([507,14]) [i] based on
- adding a parity check bit [i] based on linear OA(289, 546, F2, 18) (dual of [546, 457, 19]-code), using
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(290, 273, F2, 3, 19) (dual of [(273, 3), 729, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(290, 273, F2, 4, 19) (dual of [(273, 4), 1002, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(290, 273, F2, 5, 19) (dual of [(273, 5), 1275, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(290, 273, F2, 6, 19) (dual of [(273, 6), 1548, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(290, 273, F2, 7, 19) (dual of [(273, 7), 1821, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(290, 273, F2, 8, 19) (dual of [(273, 8), 2094, 20]-NRT-code) | [i] | ||
| 7 | Digital (71, 90, 273)-net over F2 | [i] | ||