Information on Result #701488
Linear OA(741, 55, F7, 28) (dual of [55, 14, 29]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,34,41}), C2 = C([0,25]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,34,41}) based on
- 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 = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,34,41}, and minimum distance d ≥ |{−2,−1,…,24}|+1 = 28 (BCH-bound) [i]
- linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(740, 48, F7, 28) (dual of [48, 8, 29]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,34,41}, and minimum distance d ≥ |{−2,−1,…,25}|+1 = 29 (BCH-bound) [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(71, 5, F7, 1) (dual of [5, 4, 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
- 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
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(741, 27, F7, 2, 28) (dual of [(27, 2), 13, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(741, 18, F7, 3, 28) (dual of [(18, 3), 13, 29]-NRT-code) | [i] | ||