Information on Result #675607
Linear OA(3238, 6630, F3, 41) (dual of [6630, 6392, 42]-code), using construction X applied to Ce(40) ⊂ Ce(31) based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(321, 69, F3, 8) (dual of [69, 48, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-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 OA(3239, 6631, F3, 41) (dual of [6631, 6392, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3240, 6632, F3, 41) (dual of [6632, 6392, 42]-code) | [i] | ||
| 3 | Linear OOA(3238, 6070, F3, 2, 41) (dual of [(6070, 2), 11902, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3238, 6070, F3, 3, 41) (dual of [(6070, 3), 17972, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(3238, 6070, F3, 4, 41) (dual of [(6070, 4), 24042, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(3238, 6070, F3, 5, 41) (dual of [(6070, 5), 30112, 42]-NRT-code) | [i] | ||
| 7 | Digital (197, 238, 6070)-net over F3 | [i] | ||
| 8 | Linear OA(3240, 6633, F3, 41) (dual of [6633, 6393, 42]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OOA(3238, 3315, F3, 2, 41) (dual of [(3315, 2), 6392, 42]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(3238, 2210, F3, 3, 41) (dual of [(2210, 3), 6392, 42]-NRT-code) | [i] | ||
| 11 | Linear OOA(3238, 1657, F3, 4, 41) (dual of [(1657, 4), 6390, 42]-NRT-code) | [i] | ||
| 12 | Linear OOA(3238, 1326, F3, 5, 41) (dual of [(1326, 5), 6392, 42]-NRT-code) | [i] | ||