Information on Result #712462
Linear OA(754, 74, F7, 31) (dual of [74, 20, 32]-code), using construction XX applied to C1 = C([7,31]), C2 = C([1,23]), C3 = C1 + C2 = C([7,23]), and C∩ = C1 ∩ C2 = C([1,31]) based on
- linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {7,8,…,31}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(732, 48, F7, 23) (dual of [48, 16, 24]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(726, 48, F7, 17) (dual of [48, 22, 18]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {7,8,…,23}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(79, 16, F7, 7) (dual of [16, 7, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- linear OA(76, 10, F7, 5) (dual of [10, 4, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(74, 8, F7, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,7)), using the narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [1,2], and minimum distance d ≥ |{1,2}| + |{−3,0}| = 4 (simple Roos-bound) [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 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 C([0,2]) ⊂ C([1,2]) [i] based on
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 OA(753, 73, F7, 30) (dual of [73, 20, 31]-code) | [i] | Truncation | |
| 2 | Linear OOA(754, 37, F7, 2, 31) (dual of [(37, 2), 20, 32]-NRT-code) | [i] | OOA Folding | |