Information on Result #704964
Linear OA(3142, 740, F3, 36) (dual of [740, 598, 37]-code), using construction XX applied to C1 = C([727,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([727,34]) based on
- linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,33}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3142, 728, F3, 36) (dual of [728, 586, 37]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3130, 728, F3, 34) (dual of [728, 598, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [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 OA(3148, 765, F3, 36) (dual of [765, 617, 37]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(3149, 778, F3, 36) (dual of [778, 629, 37]-code) | [i] | ||
| 3 | Linear OA(3150, 795, F3, 36) (dual of [795, 645, 37]-code) | [i] | ||
| 4 | Linear OA(3151, 816, F3, 36) (dual of [816, 665, 37]-code) | [i] | ||
| 5 | Linear OA(3152, 840, F3, 36) (dual of [840, 688, 37]-code) | [i] | ||
| 6 | Linear OOA(3142, 370, F3, 2, 36) (dual of [(370, 2), 598, 37]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3142, 246, F3, 3, 36) (dual of [(246, 3), 596, 37]-NRT-code) | [i] | ||
| 8 | Linear OOA(3142, 185, F3, 4, 36) (dual of [(185, 4), 598, 37]-NRT-code) | [i] | ||
| 9 | Linear OOA(3142, 148, F3, 5, 36) (dual of [(148, 5), 598, 37]-NRT-code) | [i] | ||