Information on Result #700724
Linear OA(337, 100, F3, 12) (dual of [100, 63, 13]-code), using construction XX applied to C1 = C({0,1,2,4,5,26,53}), C2 = C([0,8]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,26,53}) based on
- linear OA(325, 80, F3, 10) (dual of [80, 55, 11]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,26,53}, and minimum distance d ≥ |{−3,−2,…,6}|+1 = 11 (BCH-bound) [i]
- linear OA(325, 80, F3, 10) (dual of [80, 55, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(333, 80, F3, 13) (dual of [80, 47, 14]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,26,53}, and minimum distance d ≥ |{−3,−2,…,9}|+1 = 14 (BCH-bound) [i]
- linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [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(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
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(337, 50, F3, 2, 12) (dual of [(50, 2), 63, 13]-NRT-code) | [i] | OOA Folding | |