Information on Result #2761612
Linear OOA(2152, 16393, F2, 4, 18) (dual of [(16393, 4), 65420, 19]-NRT-code), using strength reduction based on linear OOA(2152, 16393, F2, 4, 19) (dual of [(16393, 4), 65420, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2152, 65572, F2, 19) (dual of [65572, 65420, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2152, 65575, F2, 19) (dual of [65575, 65423, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2152, 65575, F2, 19) (dual of [65575, 65423, 20]-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(2152, 15135, F2, 5, 18) (dual of [(15135, 5), 75523, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2152, 15135, F2, 6, 18) (dual of [(15135, 6), 90658, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2152, 15135, F2, 7, 18) (dual of [(15135, 7), 105793, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2152, 15135, F2, 8, 18) (dual of [(15135, 8), 120928, 19]-NRT-code) | [i] | ||
| 5 | Digital (134, 152, 15135)-net over F2 | [i] | ||