Information on Result #1084725
Linear OOA(360, 7174476, F3, 4, 5) (dual of [(7174476, 4), 28697844, 6]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(31, 2391492, F3, 4, 1) (dual of [(2391492, 4), 9565967, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 4, 1) for arbitrarily large s, using
- appending 3 arbitrary columns [i] based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 4, 1) for arbitrarily large s, using
- linear OOA(315, 2391492, F3, 4, 2) (dual of [(2391492, 4), 9565953, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(315, 7174453, F3, 4, 2) (dual of [(7174453, 4), 28697797, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(315, 7174453, F3, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- appending kth column [i] based on linear OA(315, 7174453, F3, 2) (dual of [7174453, 7174438, 3]-code), using
- Hamming code H(15,3) [i]
- appending kth column [i] based on linear OA(315, 7174453, F3, 2) (dual of [7174453, 7174438, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(315, 7174453, F3, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(315, 7174453, F3, 4, 2) (dual of [(7174453, 4), 28697797, 3]-NRT-code), using
- linear OOA(344, 2391492, F3, 4, 5) (dual of [(2391492, 4), 9565924, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(344, 4782985, F3, 5) (dual of [4782985, 4782941, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 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 (see above)
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(344, 4782985, F3, 5) (dual of [4782985, 4782941, 6]-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(360, 7174476, F3, 5, 5) (dual of [(7174476, 5), 35872320, 6]-NRT-code) | [i] | Appending kth Column | |