Information on Result #945345
Linear OOA(269, 687, F2, 3, 13) (dual of [(687, 3), 1992, 14]-NRT-code), using OOA 3-folding based on linear OA(269, 2061, F2, 13) (dual of [2061, 1992, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(269, 2062, F2, 13) (dual of [2062, 1993, 14]-code), using
- adding a parity check bit [i] based on linear OA(268, 2061, F2, 12) (dual of [2061, 1993, 13]-code), using
- construction X4 applied to C([0,12]) ⊂ C([1,10]) [i] based on
- linear OA(267, 2047, F2, 13) (dual of [2047, 1980, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(255, 2047, F2, 10) (dual of [2047, 1992, 11]-code), using 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(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
- dual of repetition code with length 14 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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 C([0,12]) ⊂ C([1,10]) [i] based on
- adding a parity check bit [i] based on linear OA(268, 2061, F2, 12) (dual of [2061, 1993, 13]-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(269, 687, F2, 3, 12) (dual of [(687, 3), 1992, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(270, 687, F2, 3, 13) (dual of [(687, 3), 1991, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(269, 656, F2, 4, 13) (dual of [(656, 4), 2555, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(269, 656, F2, 5, 13) (dual of [(656, 5), 3211, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(269, 656, F2, 6, 13) (dual of [(656, 6), 3867, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(269, 656, F2, 7, 13) (dual of [(656, 7), 4523, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(269, 656, F2, 8, 13) (dual of [(656, 8), 5179, 14]-NRT-code) | [i] | ||
| 8 | Digital (56, 69, 656)-net over F2 | [i] | ||