Information on Result #895244
Linear OOA(3219, 4194675, F3, 2, 18) (dual of [(4194675, 2), 8389131, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(339, 374, F3, 2, 9) (dual of [(374, 2), 709, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(339, 748, F3, 9) (dual of [748, 709, 10]-code), using
- construction XX applied to C1 = C([725,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([725,6]) [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 = {−3,−2,…,4}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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 = {−3,−2,…,6}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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), 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 (see above)
- construction XX applied to C1 = C([725,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([725,6]) [i] based on
- OOA 2-folding [i] based on linear OA(339, 748, F3, 9) (dual of [748, 709, 10]-code), using
- linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-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(3219, 2097337, F3, 4, 18) (dual of [(2097337, 4), 8389129, 19]-NRT-code) | [i] | OOA Folding | |