Information on Result #1117561
Linear OOA(3239, 4194548, F3, 5, 14) (dual of [(4194548, 5), 20972501, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(327, 247, F3, 5, 7) (dual of [(247, 5), 1208, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(327, 742, F3, 7) (dual of [742, 715, 8]-code), using
- construction XX applied to C1 = C([363,367]), C2 = C([361,365]), C3 = C1 + C2 = C([363,365]), and C∩ = C1 ∩ C2 = C([361,367]) [i] based on
- 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 = {363,364,365,366,367}, and designed minimum distance d ≥ |I|+1 = 6 [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 = {361,362,363,364,365}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- 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 = {361,362,…,367}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(313, 728, F3, 3) (dual of [728, 715, 4]-code or 728-cap in PG(12,3)), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364,365}, and designed minimum distance d ≥ |I|+1 = 4 [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([363,367]), C2 = C([361,365]), C3 = C1 + C2 = C([363,365]), and C∩ = C1 ∩ C2 = C([361,367]) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(327, 742, F3, 7) (dual of [742, 715, 8]-code), using
- linear OOA(3212, 4194301, F3, 5, 14) (dual of [(4194301, 5), 20971293, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3212, 8388602, F3, 3, 14) (dual of [(8388602, 3), 25165594, 15]-NRT-code), using
- trace code [i] based on linear OOA(9106, 4194301, F9, 3, 14) (dual of [(4194301, 3), 12582797, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(9106, 8388602, F9, 2, 14) (dual of [(8388602, 2), 16777098, 15]-NRT-code), using
- trace code [i] based on linear OOA(8153, 4194301, F81, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8153, 8388602, F81, 14) (dual of [8388602, 8388549, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OOA 2-folding [i] based on linear OA(8153, 8388602, F81, 14) (dual of [8388602, 8388549, 15]-code), using
- trace code [i] based on linear OOA(8153, 4194301, F81, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(9106, 8388602, F9, 2, 14) (dual of [(8388602, 2), 16777098, 15]-NRT-code), using
- trace code [i] based on linear OOA(9106, 4194301, F9, 3, 14) (dual of [(4194301, 3), 12582797, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3212, 8388602, F3, 3, 14) (dual of [(8388602, 3), 25165594, 15]-NRT-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
None.