Information on Result #1664441
Linear OOA(2142, 1236, F2, 6, 23) (dual of [(1236, 6), 7274, 24]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2142, 1236, F2, 3, 23) (dual of [(1236, 3), 3566, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2142, 1376, F2, 3, 23) (dual of [(1376, 3), 3986, 24]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2141, 1376, F2, 3, 23) (dual of [(1376, 3), 3987, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2141, 4128, F2, 23) (dual of [4128, 3987, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2139, 4126, F2, 23) (dual of [4126, 3987, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2139, 4126, F2, 23) (dual of [4126, 3987, 24]-code), using
- OOA 3-folding [i] based on linear OA(2141, 4128, F2, 23) (dual of [4128, 3987, 24]-code), using
- 21 times duplication [i] based on linear OOA(2141, 1376, F2, 3, 23) (dual of [(1376, 3), 3987, 24]-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(2142, 617, F2, 30, 23) (dual of [(617, 30), 18368, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |