Information on Result #1021895
Linear OOA(762, 7694807, F7, 3, 6) (dual of [(7694807, 3), 23084359, 7]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(71, 2801, F7, 3, 1) (dual of [(2801, 3), 8402, 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(71, 2801, F7, 3, 1) (dual of [(2801, 3), 8402, 2]-NRT-code) (see above)
- linear OOA(75, 2801, F7, 3, 2) (dual of [(2801, 3), 8398, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(75, 2801, F7, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
- appending kth column [i] based on linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- Hamming code H(5,7) [i]
- appending kth column [i] based on linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(75, 2801, F7, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
- linear OOA(713, 3843202, F7, 3, 3) (dual of [(3843202, 3), 11529593, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(713, 6120100, F7, 3, 3) (dual of [(6120100, 3), 18360287, 4]-NRT-code), using
- linear OOA(742, 3843202, F7, 3, 6) (dual of [(3843202, 3), 11529564, 7]-NRT-code), using
- trace code [i] based on linear OOA(4921, 1921601, F49, 3, 6) (dual of [(1921601, 3), 5764782, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- OOA 3-folding [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- trace code [i] based on linear OOA(4921, 1921601, F49, 3, 6) (dual of [(1921601, 3), 5764782, 7]-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.