Information on Result #701331
Linear OA(718, 55, F7, 10) (dual of [55, 37, 11]-code), using construction XX applied to C1 = C({1,3,4,5,6,8,9}), C2 = C([0,8]), C3 = C1 + C2 = C({1,3,4,5,6,8}), and C∩ = C1 ∩ C2 = C([0,9]) based on
- linear OA(713, 48, F7, 7) (dual of [48, 35, 8]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,3,4,5,6,8,9}, and minimum distance d ≥ |{3,4,…,9}|+1 = 8 (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(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 = {1,3,4,5,6,8}, and minimum distance d ≥ |{3,4,…,8}|+1 = 7 (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(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), 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(718, 27, F7, 2, 10) (dual of [(27, 2), 36, 11]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(718, 18, F7, 3, 10) (dual of [(18, 3), 36, 11]-NRT-code) | [i] | ||