Information on Result #813891
Linear OOA(3101, 1098, F3, 2, 22) (dual of [(1098, 2), 2095, 23]-NRT-code), using OOA 2-folding based on linear OA(3101, 2196, F3, 22) (dual of [2196, 2095, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3101, 2197, F3, 22) (dual of [2197, 2096, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) [i] based on
- 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(392, 2187, F3, 20) (dual of [2187, 2095, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(385, 2187, F3, 19) (dual of [2187, 2102, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) [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(3101, 1098, F3, 3, 22) (dual of [(1098, 3), 3193, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3101, 1098, F3, 4, 22) (dual of [(1098, 4), 4291, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3101, 1098, F3, 5, 22) (dual of [(1098, 5), 5389, 23]-NRT-code) | [i] | ||
| 4 | Digital (79, 101, 1098)-net over F3 | [i] | ||