Information on Result #700771
Linear OA(349, 94, F3, 18) (dual of [94, 45, 19]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,13,26,53}), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,13,14,26,53}) based on
- 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(339, 80, F3, 16) (dual of [80, 41, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(347, 80, F3, 19) (dual of [80, 33, 20]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,26,53}, and minimum distance d ≥ |{−3,−2,…,15}|+1 = 20 (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(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 5, F3, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
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(349, 47, F3, 2, 18) (dual of [(47, 2), 45, 19]-NRT-code) | [i] | OOA Folding | |