Information on Result #806022
Linear OOA(287, 529, F2, 2, 16) (dual of [(529, 2), 971, 17]-NRT-code), using OOA 2-folding based on linear OA(287, 1058, F2, 16) (dual of [1058, 971, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(287, 1059, F2, 16) (dual of [1059, 972, 17]-code), using
- 1 times truncation [i] based on linear OA(288, 1060, F2, 17) (dual of [1060, 972, 18]-code), using
- construction XX applied to C1 = C([1019,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1019,12]) [i] based on
- 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 = {−4,−3,…,10}, and designed minimum distance d ≥ |I|+1 = 16 [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(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [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(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- 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
- construction XX applied to C1 = C([1019,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1019,12]) [i] based on
- 1 times truncation [i] based on linear OA(288, 1060, F2, 17) (dual of [1060, 972, 18]-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(287, 509, F2, 3, 16) (dual of [(509, 3), 1440, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(287, 509, F2, 4, 16) (dual of [(509, 4), 1949, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(287, 509, F2, 5, 16) (dual of [(509, 5), 2458, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(287, 509, F2, 6, 16) (dual of [(509, 6), 2967, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(287, 509, F2, 7, 16) (dual of [(509, 7), 3476, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(287, 509, F2, 8, 16) (dual of [(509, 8), 3985, 17]-NRT-code) | [i] | ||
| 7 | Digital (71, 87, 509)-net over F2 | [i] | ||