Information on Result #714432
Linear OA(87, 67, F8, 4) (dual of [67, 60, 5]-code), using construction XX applied to C1 = C([62,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([62,2]) based on
- linear OA(85, 63, F8, 3) (dual of [63, 58, 4]-code or 63-cap in PG(4,8)), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(85, 63, F8, 3) (dual of [63, 58, 4]-code or 63-cap in PG(4,8)), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(87, 63, F8, 4) (dual of [63, 56, 5]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(80, 2, F8, 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(89, 139, F8, 4) (dual of [139, 130, 5]-code) | [i] | Varšamov–Edel Lengthening | |