Information on Result #1703444
Linear OOA(2216, 10929, F2, 8, 27) (dual of [(10929, 8), 87216, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2216, 10929, F2, 6, 27) (dual of [(10929, 6), 65358, 28]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2216, 65574, F2, 27) (dual of [65574, 65358, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 65575, F2, 27) (dual of [65575, 65359, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2216, 65575, F2, 27) (dual of [65575, 65359, 28]-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(2217, 10929, F2, 8, 27) (dual of [(10929, 8), 87215, 28]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2218, 10929, F2, 8, 27) (dual of [(10929, 8), 87214, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(2219, 10929, F2, 8, 27) (dual of [(10929, 8), 87213, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2220, 10929, F2, 8, 27) (dual of [(10929, 8), 87212, 28]-NRT-code) | [i] | ||