Information on Result #677629
Linear OA(378, 85, F3, 53) (dual of [85, 7, 54]-code), using construction XX applied to C1 = C([0,99]), C2 = C([1,105]), C3 = C1 + C2 = C([1,99]), and C∩ = C1 ∩ C2 = C([0,105]) based on
- linear OA(374, 80, F3, 50) (dual of [80, 6, 51]-code), using contraction [i] based on linear OA(3154, 160, F3, 101) (dual of [160, 6, 102]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,99], and minimum distance d ≥ |{−1,0,…,99}|+1 = 102 (BCH-bound) [i]
- linear OA(375, 80, F3, 52) (dual of [80, 5, 53]-code), using contraction [i] based on linear OA(3155, 160, F3, 105) (dual of [160, 5, 106]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,105], and designed minimum distance d ≥ |I|+1 = 106 [i]
- linear OA(376, 80, F3, 53) (dual of [80, 4, 54]-code), using contraction [i] based on linear OA(3156, 160, F3, 107) (dual of [160, 4, 108]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,105], and minimum distance d ≥ |{−5,8,21,…,−67}|+1 = 108 (BCH-bound) [i]
- linear OA(373, 80, F3, 49) (dual of [80, 7, 50]-code), using contraction [i] based on linear OA(3153, 160, F3, 99) (dual of [160, 7, 100]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,99], and designed minimum distance d ≥ |I|+1 = 100 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [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(378, 85, F3, 52) (dual of [85, 7, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(379, 86, F3, 53) (dual of [86, 7, 54]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(376, 83, F3, 51) (dual of [83, 7, 52]-code) | [i] | Truncation | |
| 4 | Linear OA(375, 82, F3, 50) (dual of [82, 7, 51]-code) | [i] | ||
| 5 | Linear OA(3170, 177, F3, 110) (dual of [177, 7, 111]-code) | [i] | Juxtaposition | |
| 6 | Linear OA(3190, 197, F3, 125) (dual of [197, 7, 126]-code) | [i] | ||
| 7 | Linear OA(3196, 203, F3, 127) (dual of [203, 7, 128]-code) | [i] | ||
| 8 | Linear OOA(378, 17, F3, 5, 53) (dual of [(17, 5), 7, 54]-NRT-code) | [i] | OOA Folding | |