Information on Result #701457
Linear OA(746, 66, F7, 27) (dual of [66, 20, 28]-code), using construction XX applied to C1 = C({1,2,3,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26}), C2 = C([0,20]), C3 = C1 + C2 = C({1,2,3,6,8,9,10,11,12,13,16,17,18,19,20}), and C∩ = C1 ∩ C2 = C([0,26]) based on
- linear OA(733, 48, F7, 21) (dual of [48, 15, 22]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26}, and minimum distance d ≥ |{6,7,…,26}|+1 = 22 (BCH-bound) [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(728, 48, F7, 18) (dual of [48, 20, 19]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,6,8,9,10,11,12,13,16,17,18,19,20}, and minimum distance d ≥ |{6,7,…,23}|+1 = 19 (BCH-bound) [i]
- 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]
- linear OA(76, 11, F7, 5) (dual of [11, 5, 6]-code), using
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C1 ⊂ C0 [i] based on
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), 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(746, 33, F7, 2, 27) (dual of [(33, 2), 20, 28]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(746, 22, F7, 3, 27) (dual of [(22, 3), 20, 28]-NRT-code) | [i] | ||