Information on Result #707163
Linear OA(4255, 270, F4, 177) (dual of [270, 15, 178]-code), using construction XX applied to C1 = C([251,170]), C2 = C([1,174]), C3 = C1 + C2 = C([1,170]), and C∩ = C1 ∩ C2 = C([251,174]) based on
- linear OA(4245, 255, F4, 175) (dual of [255, 10, 176]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,170}, and designed minimum distance d ≥ |I|+1 = 176 [i]
- linear OA(4244, 255, F4, 174) (dual of [255, 11, 175]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,174], and designed minimum distance d ≥ |I|+1 = 175 [i]
- linear OA(4249, 255, F4, 179) (dual of [255, 6, 180]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,174}, and designed minimum distance d ≥ |I|+1 = 180 [i]
- linear OA(4240, 255, F4, 170) (dual of [255, 15, 171]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,170], and designed minimum distance d ≥ |I|+1 = 171 [i]
- linear OA(45, 10, F4, 4) (dual of [10, 5, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(45, 11, F4, 4) (dual of [11, 6, 5]-code), 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(4254, 269, F4, 176) (dual of [269, 15, 177]-code) | [i] | Truncation | |
| 2 | Linear OOA(4255, 135, F4, 2, 177) (dual of [(135, 2), 15, 178]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4255, 90, F4, 3, 177) (dual of [(90, 3), 15, 178]-NRT-code) | [i] | ||