Information on Result #895333
Linear OOA(3249, 4194672, F3, 2, 21) (dual of [(4194672, 2), 8389095, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(339, 371, F3, 2, 10) (dual of [(371, 2), 703, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(339, 742, F3, 10) (dual of [742, 703, 11]-code), using
- construction XX applied to C1 = C([360,367]), C2 = C([358,365]), C3 = C1 + C2 = C([360,365]), and C∩ = C1 ∩ C2 = C([358,367]) [i] based on
- linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {360,361,…,367}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {358,359,…,365}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(337, 728, F3, 10) (dual of [728, 691, 11]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {358,359,…,367}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(325, 728, F3, 6) (dual of [728, 703, 7]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {360,361,…,365}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code) (see above)
- construction XX applied to C1 = C([360,367]), C2 = C([358,365]), C3 = C1 + C2 = C([360,365]), and C∩ = C1 ∩ C2 = C([358,367]) [i] based on
- OOA 2-folding [i] based on linear OA(339, 742, F3, 10) (dual of [742, 703, 11]-code), using
- linear OOA(3210, 4194301, F3, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3250, 4194672, F3, 2, 21) (dual of [(4194672, 2), 8389094, 22]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3249, 2097336, F3, 4, 21) (dual of [(2097336, 4), 8389095, 22]-NRT-code) | [i] | OOA Folding | |