Information on Result #805518
Linear OOA(231, 71, F2, 2, 9) (dual of [(71, 2), 111, 10]-NRT-code), using OOA 2-folding based on linear OA(231, 142, F2, 9) (dual of [142, 111, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(231, 143, F2, 9) (dual of [143, 112, 10]-code), using
- construction XX applied to C1 = C({0,1,3,63}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,3,5,63}) [i] based on
- linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,63}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
- linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,63}, and minimum distance d ≥ |{−2,−1,…,6}|+1 = 10 (BCH-bound) [i]
- linear OA(215, 127, F2, 5) (dual of [127, 112, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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, 8, F2, 1) (dual of [8, 7, 2]-code) (see above)
- construction XX applied to C1 = C({0,1,3,63}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,3,5,63}) [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(2238, 4194372, F2, 2, 18) (dual of [(4194372, 2), 8388506, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2239, 4194372, F2, 2, 19) (dual of [(4194372, 2), 8388505, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(231, 71, F2, 3, 9) (dual of [(71, 3), 182, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(231, 71, F2, 4, 9) (dual of [(71, 4), 253, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(231, 71, F2, 5, 9) (dual of [(71, 5), 324, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(231, 71, F2, 6, 9) (dual of [(71, 6), 395, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(231, 71, F2, 7, 9) (dual of [(71, 7), 466, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(231, 71, F2, 8, 9) (dual of [(71, 8), 537, 10]-NRT-code) | [i] | ||