Information on Result #701429
Linear OA(750, 75, F7, 27) (dual of [75, 25, 28]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,20,27,34,40,41}), C2 = C([1,18]), C3 = C1 + C2 = C([1,13]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,20,27,34,40,41}) based on
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,20,27,34,40,41}, and minimum distance d ≥ |{−8,−7,…,15}|+1 = 25 (BCH-bound) [i]
- linear OA(728, 48, F7, 18) (dual of [48, 20, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,20,27,34,40,41}, and minimum distance d ≥ |{−8,−7,…,18}|+1 = 28 (BCH-bound) [i]
- linear OA(723, 48, F7, 15) (dual of [48, 25, 16]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [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]
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(750, 75, F7, 26) (dual of [75, 25, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(751, 76, F7, 27) (dual of [76, 25, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(750, 37, F7, 2, 27) (dual of [(37, 2), 24, 28]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(750, 25, F7, 3, 27) (dual of [(25, 3), 25, 28]-NRT-code) | [i] | ||