Information on Result #676941
Linear OA(3228, 757, F3, 58) (dual of [757, 529, 59]-code), using construction XX applied to Ce(57) ⊂ Ce(51) ⊂ Ce(49) based on
- linear OA(3217, 729, F3, 58) (dual of [729, 512, 59]-code), using an extension Ce(57) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,57], and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(3202, 729, F3, 52) (dual of [729, 527, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3196, 729, F3, 50) (dual of [729, 533, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(38, 25, F3, 5) (dual of [25, 17, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 26, F3, 5) (dual of [26, 18, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- discarding factors / shortening the dual code based on linear OA(38, 26, F3, 5) (dual of [26, 18, 6]-code), using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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 OA(3227, 756, F3, 57) (dual of [756, 529, 58]-code) | [i] | Truncation | |
| 2 | Linear OOA(3228, 378, F3, 2, 58) (dual of [(378, 2), 528, 59]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3228, 252, F3, 3, 58) (dual of [(252, 3), 528, 59]-NRT-code) | [i] | ||
| 4 | Linear OOA(3228, 189, F3, 4, 58) (dual of [(189, 4), 528, 59]-NRT-code) | [i] | ||