Information on Result #730959
Linear OA(4130, 518, F4, 37) (dual of [518, 388, 38]-code), using trace code based on linear OA(1665, 259, F16, 37) (dual of [259, 194, 38]-code), using
- construction XX applied to C1 = C([254,34]), C2 = C([0,35]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([254,35]) [i] based on
- linear OA(1663, 255, F16, 36) (dual of [255, 192, 37]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(1663, 255, F16, 36) (dual of [255, 192, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(1665, 255, F16, 37) (dual of [255, 190, 38]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,35}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(1661, 255, F16, 35) (dual of [255, 194, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(160, 2, F16, 0) (dual of [2, 2, 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(4131, 519, F4, 37) (dual of [519, 388, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4130, 259, F4, 2, 37) (dual of [(259, 2), 388, 38]-NRT-code) | [i] | OOA Folding | |