Information on Result #1304119
Linear OA(347, 291, F3, 12) (dual of [291, 244, 13]-code), using 33 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 1, 4 times 0, 1, 8 times 0, 1, 13 times 0) based on linear OA(341, 252, F3, 12) (dual of [252, 211, 13]-code), using
- construction XX applied to C1 = C([241,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([241,10]) [i] based on
- linear OA(336, 242, F3, 11) (dual of [242, 206, 12]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(336, 242, F3, 11) (dual of [242, 206, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(341, 242, F3, 12) (dual of [242, 201, 13]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(331, 242, F3, 10) (dual of [242, 211, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 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, 5, F3, 0) (dual of [5, 5, 1]-code) (see above)
Mode: 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(347, 291, F3, 2, 12) (dual of [(291, 2), 535, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(347, 291, F3, 3, 12) (dual of [(291, 3), 826, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(347, 291, F3, 4, 12) (dual of [(291, 4), 1117, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(347, 291, F3, 5, 12) (dual of [(291, 5), 1408, 13]-NRT-code) | [i] | ||
| 5 | Digital (35, 47, 291)-net over F3 | [i] | ||