Information on Result #700782
Linear OA(354, 87, F3, 23) (dual of [87, 33, 24]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,13,14,16,17,53}), C2 = C([0,20]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,53}) based on
- linear OA(351, 80, F3, 21) (dual of [80, 29, 22]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,53}, and minimum distance d ≥ |{−1,0,…,19}|+1 = 22 (BCH-bound) [i]
- linear OA(349, 80, F3, 22) (dual of [80, 31, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(353, 80, F3, 23) (dual of [80, 27, 24]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,53}, and minimum distance d ≥ |{−1,0,…,21}|+1 = 24 (BCH-bound) [i]
- linear OA(347, 80, F3, 20) (dual of [80, 33, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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 OOA(354, 43, F3, 2, 23) (dual of [(43, 2), 32, 24]-NRT-code) | [i] | OOA Folding | |