Information on Result #677689
Linear OA(3113, 129, F3, 64) (dual of [129, 16, 65]-code), using construction XX applied to C1 = C([0,60]), C2 = C([1,66]), C3 = C1 + C2 = C([1,60]), and C∩ = C1 ∩ C2 = C([0,66]) based on
- 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(3110, 121, F3, 66) (dual of [121, 11, 67]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,66], and designed minimum distance d ≥ |I|+1 = 67 [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(3105, 121, F3, 60) (dual of [121, 16, 61]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,60], and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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
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(3113, 129, F3, 63) (dual of [129, 16, 64]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3113, 129, F3, 62) (dual of [129, 16, 63]-code) | [i] | ||
| 3 | Linear OA(3113, 129, F3, 61) (dual of [129, 16, 62]-code) | [i] | ||
| 4 | Linear OA(3113, 129, F3, 60) (dual of [129, 16, 61]-code) | [i] | ||
| 5 | Linear OA(3113, 129, F3, 59) (dual of [129, 16, 60]-code) | [i] | ||
| 6 | Linear OA(3113, 129, F3, 58) (dual of [129, 16, 59]-code) | [i] | ||
| 7 | Linear OA(3111, 127, F3, 62) (dual of [127, 16, 63]-code) | [i] | Truncation | |
| 8 | Linear OA(3110, 126, F3, 61) (dual of [126, 16, 62]-code) | [i] | ||
| 9 | Linear OA(3109, 125, F3, 60) (dual of [125, 16, 61]-code) | [i] | ||
| 10 | Linear OA(3108, 124, F3, 59) (dual of [124, 16, 60]-code) | [i] | ||
| 11 | Linear OA(3106, 122, F3, 57) (dual of [122, 16, 58]-code) | [i] | ||
| 12 | Linear OA(3132, 155, F3, 64) (dual of [155, 23, 65]-code) | [i] | Varšamov–Edel Lengthening | |
| 13 | Linear OA(3133, 157, F3, 64) (dual of [157, 24, 65]-code) | [i] | ||
| 14 | Linear OA(3134, 159, F3, 64) (dual of [159, 25, 65]-code) | [i] | ||
| 15 | Linear OA(3135, 161, F3, 64) (dual of [161, 26, 65]-code) | [i] | ||
| 16 | Linear OA(3136, 163, F3, 64) (dual of [163, 27, 65]-code) | [i] | ||
| 17 | Linear OA(3129, 150, F3, 63) (dual of [150, 21, 64]-code) | [i] | Construction X with Varšamov Bound | |
| 18 | Linear OOA(3113, 64, F3, 2, 64) (dual of [(64, 2), 15, 65]-NRT-code) | [i] | OOA Folding | |
| 19 | Linear OOA(3113, 43, F3, 3, 64) (dual of [(43, 3), 16, 65]-NRT-code) | [i] | ||