Information on Result #674609
Linear OA(3178, 531498, F3, 21) (dual of [531498, 531320, 22]-code), using construction X applied to Ce(21) ⊂ Ce(15) 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(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(39, 57, F3, 4) (dual of [57, 48, 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 OOA(3178, 265749, F3, 2, 21) (dual of [(265749, 2), 531320, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3178, 177166, F3, 3, 21) (dual of [(177166, 3), 531320, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3178, 132874, F3, 4, 21) (dual of [(132874, 4), 531318, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(3178, 106299, F3, 5, 21) (dual of [(106299, 5), 531317, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(3178, 53149, F3, 21, 21) (dual of [(53149, 21), 1115951, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |