Information on Result #805853
Linear OOA(272, 522, F2, 2, 14) (dual of [(522, 2), 972, 15]-NRT-code), using OOA 2-folding based on linear OA(272, 1044, F2, 14) (dual of [1044, 972, 15]-code), using
- 1 times truncation [i] based on linear OA(273, 1045, F2, 15) (dual of [1045, 972, 16]-code), using
- construction XX applied to C1 = C([1021,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1021,12]) [i] based on
- linear OA(261, 1023, F2, 13) (dual of [1023, 962, 14]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(261, 1023, F2, 13) (dual of [1023, 962, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(271, 1023, F2, 15) (dual of [1023, 952, 16]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1021,12]) [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(272, 389, F2, 3, 14) (dual of [(389, 3), 1095, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(272, 389, F2, 4, 14) (dual of [(389, 4), 1484, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(272, 389, F2, 5, 14) (dual of [(389, 5), 1873, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(272, 389, F2, 6, 14) (dual of [(389, 6), 2262, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(272, 389, F2, 7, 14) (dual of [(389, 7), 2651, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(272, 389, F2, 8, 14) (dual of [(389, 8), 3040, 15]-NRT-code) | [i] | ||
| 7 | Digital (58, 72, 389)-net over F2 | [i] | ||