Information on Result #704895
Linear OA(3155, 759, F3, 38) (dual of [759, 604, 39]-code), using construction XX applied to C1 = C([328,364]), C2 = C([333,365]), C3 = C1 + C2 = C([333,364]), and C∩ = C1 ∩ C2 = C([328,365]) based on
- 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 = {328,329,…,364}, and designed minimum distance d ≥ |I|+1 = 38 [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 = {333,334,…,365}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3148, 728, F3, 38) (dual of [728, 580, 39]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {328,329,…,365}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- 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 = {333,334,…,364}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- 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
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(3155, 753, F3, 2, 38) (dual of [(753, 2), 1351, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3155, 753, F3, 3, 38) (dual of [(753, 3), 2104, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3155, 753, F3, 4, 38) (dual of [(753, 4), 2857, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3155, 753, F3, 5, 38) (dual of [(753, 5), 3610, 39]-NRT-code) | [i] | ||
| 5 | Digital (117, 155, 753)-net over F3 | [i] | ||
| 6 | Linear OOA(3155, 379, F3, 2, 38) (dual of [(379, 2), 603, 39]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3155, 253, F3, 3, 38) (dual of [(253, 3), 604, 39]-NRT-code) | [i] | ||
| 8 | Linear OOA(3155, 189, F3, 4, 38) (dual of [(189, 4), 601, 39]-NRT-code) | [i] | ||