Information on Result #674585
Linear OA(3178, 531486, F3, 22) (dual of [531486, 531308, 23]-code), using construction X applied to Ce(21) ⊂ Ce(16) based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-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(3179, 531487, F3, 22) (dual of [531487, 531308, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3177, 531485, F3, 21) (dual of [531485, 531308, 22]-code) | [i] | Truncation | |
| 3 | Linear OOA(3178, 265743, F3, 2, 22) (dual of [(265743, 2), 531308, 23]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3178, 177162, F3, 3, 22) (dual of [(177162, 3), 531308, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(3178, 132871, F3, 4, 22) (dual of [(132871, 4), 531306, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(3178, 106297, F3, 5, 22) (dual of [(106297, 5), 531307, 23]-NRT-code) | [i] | ||