Information on Result #737794
Linear OA(8171, 32839, F8, 35) (dual of [32839, 32668, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,11]) based on
- linear OA(8151, 32769, F8, 35) (dual of [32769, 32618, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(8101, 32769, F8, 23) (dual of [32769, 32668, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(820, 70, F8, 11) (dual of [70, 50, 12]-code), using
- construction XX applied to C1 = C([0,9]), C2 = C([3,10]), C3 = C1 + C2 = C([3,9]), and C∩ = C1 ∩ C2 = C([0,10]) [i] based on
- linear OA(816, 63, F8, 10) (dual of [63, 47, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(815, 63, F8, 8) (dual of [63, 48, 9]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {3,4,…,10}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(818, 63, F8, 11) (dual of [63, 45, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {3,4,…,9}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(82, 5, F8, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,8)), using
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- 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
- construction XX applied to C1 = C([0,9]), C2 = C([3,10]), C3 = C1 + C2 = C([3,9]), and C∩ = C1 ∩ C2 = C([0,10]) [i] based on
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(8172, 32840, F8, 35) (dual of [32840, 32668, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8171, 16419, F8, 2, 35) (dual of [(16419, 2), 32667, 36]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8171, 10946, F8, 3, 35) (dual of [(10946, 3), 32667, 36]-NRT-code) | [i] | ||