Information on Result #2454228
Linear OOA(4950, large, F49, 2, 4), using strength reduction based on linear OOA(4950, large, F49, 2, 8), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(491, 50, F49, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(491, s, F49, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(491, s, F49, 2, 1) for arbitrarily large s, using
- linear OOA(492, 50, F49, 2, 2) (dual of [(50, 2), 98, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;98,49) [i]
- linear OOA(495, 2882402, F49, 2, 2) (dual of [(2882402, 2), 5764799, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(495, 5884901, F49, 2, 2) (dual of [(5884901, 2), 11769797, 3]-NRT-code), using
- appending kth column [i] based on linear OA(495, 5884901, F49, 2) (dual of [5884901, 5884896, 3]-code), using
- Hamming code H(5,49) [i]
- appending kth column [i] based on linear OA(495, 5884901, F49, 2) (dual of [5884901, 5884896, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(495, 5884901, F49, 2, 2) (dual of [(5884901, 2), 11769797, 3]-NRT-code), using
- 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
- linear OOA(4929, 2882402, F49, 2, 8) (dual of [(2882402, 2), 5764775, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 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 2-folding [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- linear OOA(491, 50, F49, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.