Information on Result #814716
Linear OOA(3138, 1113, F3, 2, 28) (dual of [(1113, 2), 2088, 29]-NRT-code), using OOA 2-folding based on linear OA(3138, 2226, F3, 28) (dual of [2226, 2088, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(311, 39, F3, 5) (dual of [39, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 40, F3, 5) (dual of [40, 29, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(37, 14, F3, 5) (dual of [14, 7, 6]-code), using
- extended quadratic residue code Qe(14,3) [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(311, 40, F3, 5) (dual of [40, 29, 6]-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(3138, 1113, F3, 2, 27) (dual of [(1113, 2), 2088, 28]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3140, 1114, F3, 2, 28) (dual of [(1114, 2), 2088, 29]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(3142, 1115, F3, 2, 28) (dual of [(1115, 2), 2088, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3139, 1113, F3, 2, 28) (dual of [(1113, 2), 2087, 29]-NRT-code) | [i] | OOA Duplication | |