Information on Result #706931
Linear OA(4130, 276, F4, 45) (dual of [276, 146, 46]-code), using construction XX applied to C1 = C([251,38]), C2 = C([0,40]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([251,40]) based on
- linear OA(4121, 255, F4, 43) (dual of [255, 134, 44]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(4113, 255, F4, 41) (dual of [255, 142, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4125, 255, F4, 45) (dual of [255, 130, 46]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4109, 255, F4, 39) (dual of [255, 146, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-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 OA(4131, 277, F4, 45) (dual of [277, 146, 46]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4130, 138, F4, 2, 45) (dual of [(138, 2), 146, 46]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4130, 92, F4, 3, 45) (dual of [(92, 3), 146, 46]-NRT-code) | [i] | ||