Information on Result #1596461
Linear OOA(2214, 1345, F2, 4, 35) (dual of [(1345, 4), 5166, 36]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2214, 1345, F2, 3, 35) (dual of [(1345, 3), 3821, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2214, 1376, F2, 3, 35) (dual of [(1376, 3), 3914, 36]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2213, 1376, F2, 3, 35) (dual of [(1376, 3), 3915, 36]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2213, 4128, F2, 35) (dual of [4128, 3915, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2211, 4126, F2, 35) (dual of [4126, 3915, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-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
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2211, 4126, F2, 35) (dual of [4126, 3915, 36]-code), using
- OOA 3-folding [i] based on linear OA(2213, 4128, F2, 35) (dual of [4128, 3915, 36]-code), using
- 21 times duplication [i] based on linear OOA(2213, 1376, F2, 3, 35) (dual of [(1376, 3), 3915, 36]-NRT-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(2214, 672, F2, 7, 35) (dual of [(672, 7), 4490, 36]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2214, 672, F2, 8, 35) (dual of [(672, 8), 5162, 36]-NRT-code) | [i] | ||