Information on Result #2921417
Linear OOA(2198, 349533, F2, 6, 19) (dual of [(349533, 6), 2097000, 20]-NRT-code), using 21 times duplication based on linear OOA(2197, 349533, F2, 6, 19) (dual of [(349533, 6), 2097001, 20]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2197, 2097198, F2, 19) (dual of [2097198, 2097001, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2197, 2097201, F2, 19) (dual of [2097201, 2097004, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-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(2197, 2097201, F2, 19) (dual of [2097201, 2097004, 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(2198, 346593, F2, 7, 19) (dual of [(346593, 7), 2425953, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2198, 346593, F2, 8, 19) (dual of [(346593, 8), 2772546, 20]-NRT-code) | [i] | ||
| 3 | Digital (179, 198, 346593)-net over F2 | [i] | ||