Information on Result #705716
Linear OA(3237, 782, F3, 57) (dual of [782, 545, 58]-code), using construction XX applied to C1 = C([342,392]), C2 = C([336,386]), C3 = C1 + C2 = C([342,386]), and C∩ = C1 ∩ C2 = C([336,392]) based on
- linear OA(3202, 728, F3, 51) (dual of [728, 526, 52]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,392}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3202, 728, F3, 51) (dual of [728, 526, 52]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,386}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3217, 728, F3, 57) (dual of [728, 511, 58]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,392}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(3181, 728, F3, 45) (dual of [728, 547, 46]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,386}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(38, 27, F3, 5) (dual of [27, 19, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(319, 27, F3, 13) (dual of [27, 8, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- nonexistence of linear OA(318, 22, F3, 13) (dual of [22, 4, 14]-code), because
- 1 times truncation [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- linear OA(319, 27, F3, 13) (dual of [27, 8, 14]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(38, 27, F3, 5) (dual of [27, 19, 6]-code) (see above)
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(3237, 391, F3, 2, 57) (dual of [(391, 2), 545, 58]-NRT-code) | [i] | OOA Folding | |