Information on Result #906774
Linear OOA(2720, 7174494, F27, 2, 4) (dual of [(7174494, 2), 14348968, 5]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(270, s, F27, 2, 0) for arbitrarily large s, using
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(270, 265722, F27, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(271, 265722, F27, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- linear OOA(271, 265722, F27, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
- linear OOA(275, 265722, F27, 2, 2) (dual of [(265722, 2), 531439, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(275, 551881, F27, 2, 2) (dual of [(551881, 2), 1103757, 3]-NRT-code), using
- appending kth column [i] based on linear OA(275, 551881, F27, 2) (dual of [551881, 551876, 3]-code), using
- Hamming code H(5,27) [i]
- appending kth column [i] based on linear OA(275, 551881, F27, 2) (dual of [551881, 551876, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(275, 551881, F27, 2, 2) (dual of [(551881, 2), 1103757, 3]-NRT-code), using
- linear OOA(2713, 265722, F27, 2, 4) (dual of [(265722, 2), 531431, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2713, 531441, F27, 4) (dual of [531441, 531428, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(279, 531441, F27, 3) (dual of [531441, 531432, 4]-code or 531441-cap in PG(8,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- OOA 2-folding [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-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(2720, 7174493, F27, 6, 4) (dual of [(7174493, 6), 43046938, 5]-NRT-code) | [i] | OOA Stacking with Additional Row | |