Information on Result #2236030
Linear OA(461, 77, F4, 33) (dual of [77, 16, 34]-code), using 1 times truncation based on linear OA(462, 78, F4, 34) (dual of [78, 16, 35]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}) [i] based on
- linear OA(453, 63, F4, 31) (dual of [63, 10, 32]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}, and minimum distance d ≥ |{−4,−3,…,26}|+1 = 32 (BCH-bound) [i]
- linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(456, 63, F4, 34) (dual of [63, 7, 35]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}, and minimum distance d ≥ |{−4,−3,…,29}|+1 = 35 (BCH-bound) [i]
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)), using
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [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 OA(4136, 150, F4, 67) (dual of [150, 14, 68]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(4135, 148, F4, 67) (dual of [148, 13, 68]-code) | [i] | ||
| 3 | Linear OA(4134, 146, F4, 67) (dual of [146, 12, 68]-code) | [i] | ||
| 4 | Linear OA(4133, 144, F4, 67) (dual of [144, 11, 68]-code) | [i] | ||
| 5 | Linear OOA(461, 38, F4, 2, 33) (dual of [(38, 2), 15, 34]-NRT-code) | [i] | OOA Folding | |