Information on Result #701326
Linear OA(719, 58, F7, 10) (dual of [58, 39, 11]-code), using construction XX applied to C1 = C({1,4,5,6,8,9}), C2 = C([0,8]), C3 = C1 + C2 = C({1,4,5,6,8}), and C∩ = C1 ∩ C2 = C([0,9]) based on
- linear OA(711, 48, F7, 6) (dual of [48, 37, 7]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,4,5,6,8,9}, and minimum distance d ≥ |{4,5,…,9}|+1 = 7 (BCH-bound) [i]
- linear OA(714, 48, F7, 9) (dual of [48, 34, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(716, 48, F7, 10) (dual of [48, 32, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(79, 48, F7, 5) (dual of [48, 39, 6]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,4,5,6,8}, and minimum distance d ≥ |{4,5,6,7,8}|+1 = 6 (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, 8, F7, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,7) or 8-cap in PG(2,7)), using
- extended Reed–Solomon code RSe(5,7) [i]
- oval in PG(2, 7) [i]
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(719, 29, F7, 2, 10) (dual of [(29, 2), 39, 11]-NRT-code) | [i] | OOA Folding | |