Information on Result #1631722
Linear OOA(2123, 2097157, F2, 5, 11) (dual of [(2097157, 5), 10485662, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2123, 2097157, F2, 4, 11) (dual of [(2097157, 4), 8388505, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(27, 7, F2, 4, 5) (dual of [(7, 4), 21, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 7, 7)-net over F2, using
- linear OOA(2116, 2097150, F2, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2116, 8388600, F2, 11) (dual of [8388600, 8388484, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2116, large, F2, 11) (dual of [large, large−116, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(2116, large, F2, 11) (dual of [large, large−116, 12]-code), using
- OOA 4-folding [i] based on linear OA(2116, 8388600, F2, 11) (dual of [8388600, 8388484, 12]-code), using
- linear OOA(27, 7, F2, 4, 5) (dual of [(7, 4), 21, 6]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2123, 2097156, F2, 6, 11) (dual of [(2097156, 6), 12582813, 12]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(2123, 2097156, F2, 7, 11) (dual of [(2097156, 7), 14679969, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(2123, 2097156, F2, 8, 11) (dual of [(2097156, 8), 16777125, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(2123, 2097156, F2, 15, 11) (dual of [(2097156, 15), 31457217, 12]-NRT-code) | [i] | ||