Information on Result #1304682
Linear OA(3141, 832, F3, 33) (dual of [832, 691, 34]-code), using 81 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 20 times 0) based on linear OA(3130, 740, F3, 33) (dual of [740, 610, 34]-code), using
- construction XX applied to C1 = C([727,30]), C2 = C([0,31]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([727,31]) [i] based on
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3130, 728, F3, 33) (dual of [728, 598, 34]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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: 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(3141, 832, F3, 2, 33) (dual of [(832, 2), 1523, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3141, 832, F3, 3, 33) (dual of [(832, 3), 2355, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3141, 832, F3, 4, 33) (dual of [(832, 4), 3187, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3141, 832, F3, 5, 33) (dual of [(832, 5), 4019, 34]-NRT-code) | [i] | ||
| 5 | Digital (108, 141, 832)-net over F3 | [i] | ||