Information on Result #2666497
Linear OOA(260, 688, F2, 3, 11) (dual of [(688, 3), 2004, 12]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(257, 687, F2, 3, 11) (dual of [(687, 3), 2004, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(257, 2061, F2, 11) (dual of [2061, 2004, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(245, 2048, F2, 9) (dual of [2048, 2003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(212, 13, F2, 11) (dual of [13, 1, 12]-code), using
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- dual of repetition code with length 13 [i]
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
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(260, 688, F2, 4, 11) (dual of [(688, 4), 2692, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(260, 688, F2, 5, 11) (dual of [(688, 5), 3380, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(260, 688, F2, 6, 11) (dual of [(688, 6), 4068, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(260, 688, F2, 7, 11) (dual of [(688, 7), 4756, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(260, 688, F2, 8, 11) (dual of [(688, 8), 5444, 12]-NRT-code) | [i] | ||
| 6 | Digital (49, 60, 688)-net over F2 | [i] | ||