Information on Result #704926
Linear OA(3144, 748, F3, 36) (dual of [748, 604, 37]-code), using construction XX applied to C1 = C([725,31]), C2 = C([0,33]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([725,33]) 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 = {−3,−2,…,31}, and designed minimum distance d ≥ |I|+1 = 36 [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(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,33}, and designed minimum distance d ≥ |I|+1 = 38 [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(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (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(3145, 749, F3, 36) (dual of [749, 604, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3144, 658, F3, 2, 36) (dual of [(658, 2), 1172, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3144, 658, F3, 3, 36) (dual of [(658, 3), 1830, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3144, 658, F3, 4, 36) (dual of [(658, 4), 2488, 37]-NRT-code) | [i] | ||
| 5 | Linear OOA(3144, 658, F3, 5, 36) (dual of [(658, 5), 3146, 37]-NRT-code) | [i] | ||
| 6 | Digital (108, 144, 658)-net over F3 | [i] | ||
| 7 | Linear OA(3148, 766, F3, 36) (dual of [766, 618, 37]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(3149, 779, F3, 36) (dual of [779, 630, 37]-code) | [i] | ||
| 9 | Linear OA(3150, 796, F3, 36) (dual of [796, 646, 37]-code) | [i] | ||
| 10 | Linear OA(3151, 817, F3, 36) (dual of [817, 666, 37]-code) | [i] | ||
| 11 | Linear OOA(3144, 374, F3, 2, 36) (dual of [(374, 2), 604, 37]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3144, 249, F3, 3, 36) (dual of [(249, 3), 603, 37]-NRT-code) | [i] | ||
| 13 | Linear OOA(3144, 187, F3, 4, 36) (dual of [(187, 4), 604, 37]-NRT-code) | [i] | ||