Information on Result #700760
Linear OA(346, 95, F3, 17) (dual of [95, 49, 18]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,26,53}), C2 = C([0,13]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,13,26,53}) based on
- linear OA(339, 80, F3, 16) (dual of [80, 41, 17]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,26,53}, and minimum distance d ≥ |{−3,−2,…,12}|+1 = 17 (BCH-bound) [i]
- linear OA(335, 80, F3, 14) (dual of [80, 45, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(343, 80, F3, 17) (dual of [80, 37, 18]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,26,53}, and minimum distance d ≥ |{−3,−2,…,13}|+1 = 18 (BCH-bound) [i]
- linear OA(331, 80, F3, 13) (dual of [80, 49, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(33, 11, F3, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- 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
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(347, 98, F3, 17) (dual of [98, 51, 18]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OOA(346, 47, F3, 2, 17) (dual of [(47, 2), 48, 18]-NRT-code) | [i] | OOA Folding | |