Information on Result #714983
Linear OA(828, 524, F8, 10) (dual of [524, 496, 11]-code), using construction XX applied to C1 = C([0,8]), C2 = C([4,9]), C3 = C1 + C2 = C([4,8]), and C∩ = C1 ∩ C2 = C([0,9]) based on
- linear OA(822, 511, F8, 9) (dual of [511, 489, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(818, 511, F8, 6) (dual of [511, 493, 7]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {4,5,…,9}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(815, 511, F8, 5) (dual of [511, 496, 6]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {4,5,6,7,8}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(83, 10, F8, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,8) or 10-cap in PG(2,8)), using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 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
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(828, 262, F8, 2, 10) (dual of [(262, 2), 496, 11]-NRT-code) | [i] | OOA Folding | |