Information on Result #1584298
Linear OOA(235, 131090, F2, 4, 4) (dual of [(131090, 4), 524325, 5]-NRT-code), using appending kth column based on linear OOA(235, 131090, F2, 3, 4) (dual of [(131090, 3), 393235, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(235, 131090, F2, 4) (dual of [131090, 131055, 5]-code), using
- 1 times truncation [i] based on linear OA(236, 131091, F2, 5) (dual of [131091, 131055, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(235, 131072, F2, 5) (dual of [131072, 131037, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(218, 131072, F2, 3) (dual of [131072, 131054, 4]-code or 131072-cap in PG(17,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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 X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(236, 131091, F2, 5) (dual of [131091, 131055, 6]-code), using
Mode: 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(235, 131090, F2, 5, 4) (dual of [(131090, 5), 655415, 5]-NRT-code) | [i] | Appending Arbitrary Columns | |
| 2 | Linear OOA(235, 131090, F2, 6, 4) (dual of [(131090, 6), 786505, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(235, 131090, F2, 7, 4) (dual of [(131090, 7), 917595, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(235, 131090, F2, 8, 4) (dual of [(131090, 8), 1048685, 5]-NRT-code) | [i] | ||
| 5 | Digital (31, 35, 131090)-net over F2 | [i] | Net Defined by OOA | |