Information on Result #701405
Linear OA(734, 59, F7, 20) (dual of [59, 25, 21]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,34,41}), C2 = C([1,17]), C3 = C1 + C2 = C([1,13]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,34,41}) based on
- 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 = {0,1,2,3,4,5,6,8,9,10,11,12,13,34,41}, and minimum distance d ≥ |{−2,−1,…,15}|+1 = 19 (BCH-bound) [i]
- linear OA(726, 48, F7, 17) (dual of [48, 22, 18]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,34,41}, and minimum distance d ≥ |{−2,−1,…,17}|+1 = 21 (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(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(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-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(734, 29, F7, 2, 20) (dual of [(29, 2), 24, 21]-NRT-code) | [i] | OOA Folding | |