Information on Result #706975
Linear OA(4137, 275, F4, 47) (dual of [275, 138, 48]-code), using construction XX applied to C1 = C([251,41]), C2 = C([0,42]), C3 = C1 + C2 = C([0,41]), and C∩ = C1 ∩ C2 = C([251,42]) based on
- linear OA(4129, 255, F4, 46) (dual of [255, 126, 47]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,41}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4121, 255, F4, 43) (dual of [255, 134, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(4133, 255, F4, 47) (dual of [255, 122, 48]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(4117, 255, F4, 42) (dual of [255, 138, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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(4137, 137, F4, 2, 47) (dual of [(137, 2), 137, 48]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4137, 91, F4, 3, 47) (dual of [(91, 3), 136, 48]-NRT-code) | [i] | ||