Information on Result #703877
Linear OA(370, 376, F3, 18) (dual of [376, 306, 19]-code), using construction XX applied to C1 = C([363,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([363,16]) based on
- linear OA(364, 364, F3, 17) (dual of [364, 300, 18]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(364, 364, F3, 17) (dual of [364, 300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 364 | 36−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(370, 364, F3, 18) (dual of [364, 294, 19]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(358, 364, F3, 16) (dual of [364, 306, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 364 | 36−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code) (see above)
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(370, 375, F3, 2, 18) (dual of [(375, 2), 680, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(370, 375, F3, 3, 18) (dual of [(375, 3), 1055, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(370, 375, F3, 4, 18) (dual of [(375, 4), 1430, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(370, 375, F3, 5, 18) (dual of [(375, 5), 1805, 19]-NRT-code) | [i] | ||
| 5 | Digital (52, 70, 375)-net over F3 | [i] | ||
| 6 | Linear OA(371, 383, F3, 18) (dual of [383, 312, 19]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(370, 188, F3, 2, 18) (dual of [(188, 2), 306, 19]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(370, 125, F3, 3, 18) (dual of [(125, 3), 305, 19]-NRT-code) | [i] | ||