Information on Result #701363
Linear OA(725, 55, F7, 14) (dual of [55, 30, 15]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,34,41}), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,34,41}) based on
- linear OA(722, 48, F7, 13) (dual of [48, 26, 14]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,34,41}, and minimum distance d ≥ |{−2,−1,…,10}|+1 = 14 (BCH-bound) [i]
- linear OA(720, 48, F7, 12) (dual of [48, 28, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(724, 48, F7, 14) (dual of [48, 24, 15]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,34,41}, and minimum distance d ≥ |{−2,−1,…,11}|+1 = 15 (BCH-bound) [i]
- linear OA(718, 48, F7, 11) (dual of [48, 30, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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(725, 27, F7, 2, 14) (dual of [(27, 2), 29, 15]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(725, 18, F7, 3, 14) (dual of [(18, 3), 29, 15]-NRT-code) | [i] | ||