Information on Result #814031
Linear OOA(3123, 3286, F3, 2, 23) (dual of [(3286, 2), 6449, 24]-NRT-code), using OOA 2-folding based on linear OA(3123, 6572, F3, 23) (dual of [6572, 6449, 24]-code), using
- construction XX applied to Ce(22) ⊂ Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3105, 6561, F3, 20) (dual of [6561, 6456, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3123, 3179, F3, 3, 23) (dual of [(3179, 3), 9414, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3123, 3179, F3, 4, 23) (dual of [(3179, 4), 12593, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(3123, 3179, F3, 5, 23) (dual of [(3179, 5), 15772, 24]-NRT-code) | [i] | ||
| 4 | Digital (100, 123, 3179)-net over F3 | [i] | ||