Information on Result #1021888
Linear OOA(791, 7686820, F7, 3, 8) (dual of [(7686820, 3), 23060369, 9]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(71, 8, F7, 3, 1) (dual of [(8, 3), 23, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 3, 1) for arbitrarily large s, using
- linear OOA(72, 8, F7, 3, 2) (dual of [(8, 3), 22, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;22,7) [i]
- linear OOA(74, 400, F7, 3, 2) (dual of [(400, 3), 1196, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(74, 400, F7, 2, 2) (dual of [(400, 2), 796, 3]-NRT-code), using
- appending kth column [i] based on linear OA(74, 400, F7, 2) (dual of [400, 396, 3]-code), using
- Hamming code H(4,7) [i]
- appending kth column [i] based on linear OA(74, 400, F7, 2) (dual of [400, 396, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(74, 400, F7, 2, 2) (dual of [(400, 2), 796, 3]-NRT-code), using
- linear OOA(726, 3843202, F7, 3, 4) (dual of [(3843202, 3), 11529580, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(726, 5764803, F7, 3, 4) (dual of [(5764803, 3), 17294383, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(726, 5764804, F7, 2, 4) (dual of [(5764804, 2), 11529582, 5]-NRT-code), using
- trace code [i] based on linear OOA(4913, 2882402, F49, 2, 4) (dual of [(2882402, 2), 5764791, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- OOA 2-folding [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- trace code [i] based on linear OOA(4913, 2882402, F49, 2, 4) (dual of [(2882402, 2), 5764791, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(726, 5764804, F7, 2, 4) (dual of [(5764804, 2), 11529582, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(726, 5764803, F7, 3, 4) (dual of [(5764803, 3), 17294383, 5]-NRT-code), using
- linear OOA(758, 3843202, F7, 3, 8) (dual of [(3843202, 3), 11529548, 9]-NRT-code), using
- trace code [i] based on linear OOA(4929, 1921601, F49, 3, 8) (dual of [(1921601, 3), 5764774, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4929, 5764803, F49, 8) (dual of [5764803, 5764774, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code) (see above)
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- OOA 3-folding [i] based on linear OA(4929, 5764803, F49, 8) (dual of [5764803, 5764774, 9]-code), using
- trace code [i] based on linear OOA(4929, 1921601, F49, 3, 8) (dual of [(1921601, 3), 5764774, 9]-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.