Information on Result #815510
Linear OOA(3179, 3286, F3, 2, 34) (dual of [(3286, 2), 6393, 35]-NRT-code), using OOA 2-folding based on linear OA(3179, 6572, F3, 34) (dual of [6572, 6393, 35]-code), using
- construction XX applied to Ce(33) ⊂ Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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]
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(3179, 3260, F3, 3, 34) (dual of [(3260, 3), 9601, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3179, 3260, F3, 4, 34) (dual of [(3260, 4), 12861, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3179, 3260, F3, 5, 34) (dual of [(3260, 5), 16121, 35]-NRT-code) | [i] | ||
| 4 | Digital (145, 179, 3260)-net over F3 | [i] | ||