Information on Result #676183
Linear OA(3174, 2209, F3, 36) (dual of [2209, 2035, 37]-code), using construction XX applied to Ce(36) ⊂ Ce(33) ⊂ Ce(31) based on
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(31, 18, F3, 1) (dual of [18, 17, 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(31, 4, F3, 1) (dual of [4, 3, 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 (see above)
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(3174, 1780, F3, 2, 36) (dual of [(1780, 2), 3386, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3174, 1780, F3, 3, 36) (dual of [(1780, 3), 5166, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3174, 1780, F3, 4, 36) (dual of [(1780, 4), 6946, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3174, 1780, F3, 5, 36) (dual of [(1780, 5), 8726, 37]-NRT-code) | [i] | ||
| 5 | Digital (138, 174, 1780)-net over F3 | [i] | ||
| 6 | Linear OOA(3174, 1104, F3, 2, 36) (dual of [(1104, 2), 2034, 37]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3174, 736, F3, 3, 36) (dual of [(736, 3), 2034, 37]-NRT-code) | [i] | ||
| 8 | Linear OOA(3174, 552, F3, 4, 36) (dual of [(552, 4), 2034, 37]-NRT-code) | [i] | ||