Information on Result #700949
Linear OA(3123, 138, F3, 70) (dual of [138, 15, 71]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,13,16,17,19,20,22,25,26,31,34,35,38,40,67}), C2 = C([0,61]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([0,67]) based on
- linear OA(3111, 121, F3, 65) (dual of [121, 10, 66]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {0,1,2,4,5,7,8,10,11,13,16,17,19,20,22,25,26,31,34,35,38,40,67}, and minimum distance d ≥ |{−4,−3,…,60}|+1 = 66 (BCH-bound) [i]
- linear OA(3111, 121, F3, 68) (dual of [121, 10, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,66], and minimum distance d ≥ |{−1,0,…,66}|+1 = 69 (BCH-bound) [i]
- linear OA(3116, 121, F3, 80) (dual of [121, 5, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,75], and minimum distance d ≥ |{5,15,25,…,−52}|+1 = 81 (BCH-bound) [i]
- linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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(36, 11, F3, 5) (dual of [11, 5, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- discarding factors / shortening the dual code based on linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-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 OA(3123, 138, F3, 69) (dual of [138, 15, 70]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3122, 137, F3, 69) (dual of [137, 15, 70]-code) | [i] | Truncation | |
| 3 | Linear OOA(3123, 69, F3, 2, 70) (dual of [(69, 2), 15, 71]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3123, 46, F3, 3, 70) (dual of [(46, 3), 15, 71]-NRT-code) | [i] | ||
| 5 | Linear OOA(3123, 27, F3, 5, 70) (dual of [(27, 5), 12, 71]-NRT-code) | [i] | ||