Information on Result #701150
Linear OA(427, 94, F4, 10) (dual of [94, 67, 11]-code), using construction XX applied to C1 = C({2,5,6,14,17,21}), C2 = C({2,5,6,7,14,17}), C3 = C1 + C2 = C({2,5,6,14,17}), and C∩ = C1 ∩ C2 = C({2,5,6,7,14,17,21}) based on
- linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,20}|+1 = 10 (BCH-bound) [i]
- linear OA(422, 85, F4, 8) (dual of [85, 63, 9]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,7,14,17}, and minimum distance d ≥ |{2,5,8,…,23}|+1 = 9 (BCH-bound) [i]
- linear OA(426, 85, F4, 10) (dual of [85, 59, 11]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,7,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,23}|+1 = 11 (BCH-bound) [i]
- linear OA(418, 85, F4, 7) (dual of [85, 67, 8]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17}, and minimum distance d ≥ |{2,5,8,…,20}|+1 = 8 (BCH-bound) [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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(428, 95, F4, 10) (dual of [95, 67, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4252, 65627, F4, 38) (dual of [65627, 65375, 39]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 3 | Linear OOA(427, 47, F4, 2, 10) (dual of [(47, 2), 67, 11]-NRT-code) | [i] | OOA Folding | |