Information on Result #714876
Linear OA(872, 84, F8, 51) (dual of [84, 12, 52]-code), using construction XX applied to C1 = C([55,36]), C2 = C([0,44]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([55,44]) based on
- linear OA(855, 63, F8, 45) (dual of [63, 8, 46]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−8,−7,…,36}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(855, 63, F8, 45) (dual of [63, 8, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(859, 63, F8, 53) (dual of [63, 4, 54]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−8,−7,…,44}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(849, 63, F8, 37) (dual of [63, 14, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(85, 9, F8, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,8)), using
- extended Reed–Solomon code RSe(4,8) [i]
- linear OA(88, 12, F8, 7) (dual of [12, 4, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(88, 14, F8, 7) (dual of [14, 6, 8]-code), using
- extended algebraic-geometric code AGe(F,6P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- discarding factors / shortening the dual code based on linear OA(88, 14, F8, 7) (dual of [14, 6, 8]-code), 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.
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(870, 82, F8, 49) (dual of [82, 12, 50]-code) | [i] | Truncation | |
| 2 | Linear OOA(872, 42, F8, 2, 51) (dual of [(42, 2), 12, 52]-NRT-code) | [i] | OOA Folding | |