Information on Result #895162
Linear OOA(3183, 4194671, F3, 2, 16) (dual of [(4194671, 2), 8389159, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(332, 370, F3, 2, 8) (dual of [(370, 2), 708, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(332, 740, F3, 8) (dual of [740, 708, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(332, 741, F3, 8) (dual of [741, 709, 9]-code), using
- construction XX applied to C1 = C([358,364]), C2 = C([360,365]), C3 = C1 + C2 = C([360,364]), and C∩ = C1 ∩ C2 = C([358,365]) [i] based on
- linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {358,359,…,364}, and designed minimum distance d ≥ |I|+1 = 8 [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(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(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {360,361,362,363,364}, and designed minimum distance d ≥ |I|+1 = 6 [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(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([358,364]), C2 = C([360,365]), C3 = C1 + C2 = C([360,364]), and C∩ = C1 ∩ C2 = C([358,365]) [i] based on
- discarding factors / shortening the dual code based on linear OA(332, 741, F3, 8) (dual of [741, 709, 9]-code), using
- OOA 2-folding [i] based on linear OA(332, 740, F3, 8) (dual of [740, 708, 9]-code), using
- linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-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(3183, 2097335, F3, 4, 16) (dual of [(2097335, 4), 8389157, 17]-NRT-code) | [i] | OOA Folding | |