Information on Result #906771
Linear OOA(2726, 7174602, F27, 2, 5) (dual of [(7174602, 2), 14349178, 6]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 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, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(270, 265726, F27, 2, 0) (dual of [(265726, 2), 531452, 1]-NRT-code) (see above)
- linear OOA(271, 265726, F27, 2, 1) (dual of [(265726, 2), 531451, 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, 265726, F27, 2, 1) (dual of [(265726, 2), 531451, 2]-NRT-code) (see above)
- linear OOA(271, 265726, F27, 2, 1) (dual of [(265726, 2), 531451, 2]-NRT-code) (see above)
- linear OOA(275, 265726, F27, 2, 2) (dual of [(265726, 2), 531447, 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(2718, 265726, F27, 2, 5) (dual of [(265726, 2), 531434, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2718, 531452, F27, 5) (dual of [531452, 531434, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(2717, 531442, F27, 5) (dual of [531442, 531425, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(279, 531442, F27, 3) (dual of [531442, 531433, 4]-code or 531442-cap in PG(8,27)), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(279, 10, F27, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,27)), using
- dual of repetition code with length 10 [i]
- linear OA(271, 10, F27, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding [i] based on linear OA(2718, 531452, F27, 5) (dual of [531452, 531434, 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(2726, 7174601, F27, 6, 5) (dual of [(7174601, 6), 43047580, 6]-NRT-code) | [i] | OOA Stacking with Additional Row | |