Information on Result #701393
Linear OA(730, 56, F7, 18) (dual of [56, 26, 19]-code), using construction XX applied to C1 = C({1,2,4,5,6,8,9,10,11,12,13,16,17}), C2 = C([0,16]), C3 = C1 + C2 = C({1,2,4,5,6,8,9,10,11,12,13,16}), and C∩ = C1 ∩ C2 = C([0,17]) based on
- linear OA(724, 48, F7, 14) (dual of [48, 24, 15]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,4,5,6,8,9,10,11,12,13,16,17}, and minimum distance d ≥ |{4,5,…,17}|+1 = 15 (BCH-bound) [i]
- linear OA(725, 48, F7, 17) (dual of [48, 23, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(727, 48, F7, 18) (dual of [48, 21, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(722, 48, F7, 13) (dual of [48, 26, 14]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,4,5,6,8,9,10,11,12,13,16}, and minimum distance d ≥ |{4,5,…,16}|+1 = 14 (BCH-bound) [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(73, 6, F7, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,7) or 6-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(730, 28, F7, 2, 18) (dual of [(28, 2), 26, 19]-NRT-code) | [i] | OOA Folding | |