Information on Result #1703604
Linear OOA(2218, 87389, F2, 8, 22) (dual of [(87389, 8), 698894, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2218, 87389, F2, 6, 22) (dual of [(87389, 6), 524116, 23]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2218, 524334, F2, 22) (dual of [524334, 524116, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2216, 524332, F2, 22) (dual of [524332, 524116, 23]-code), using
- 1 times truncation [i] based on linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-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(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2216, 524332, F2, 22) (dual of [524332, 524116, 23]-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(2219, 87389, F2, 8, 22) (dual of [(87389, 8), 698893, 23]-NRT-code) | [i] | OOA Duplication | |