Information on Result #735246
Linear OA(8171, 6978, F81, 25) (dual of [6978, 6907, 26]-code), using (u, u+v)-construction based on
- linear OA(8122, 415, F81, 12) (dual of [415, 393, 13]-code), using
- construction XX applied to C1 = C([36,46]), C2 = C([35,44]), C3 = C1 + C2 = C([36,44]), and C∩ = C1 ∩ C2 = C([35,46]) [i] based on
- linear OA(8119, 410, F81, 11) (dual of [410, 391, 12]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {36,37,…,46}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(8119, 410, F81, 10) (dual of [410, 391, 11]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,44}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(8121, 410, F81, 12) (dual of [410, 389, 13]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,46}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(8117, 410, F81, 9) (dual of [410, 393, 10]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {36,37,…,44}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(811, 3, F81, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- Reed–Solomon code RS(80,81) [i]
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([36,46]), C2 = C([35,44]), C3 = C1 + C2 = C([36,44]), and C∩ = C1 ∩ C2 = C([35,46]) [i] based on
- linear OA(8149, 6563, F81, 25) (dual of [6563, 6514, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(8149, 6561, F81, 25) (dual of [6561, 6512, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code) (see above)
- construction X applied to Ce(24) ⊂ Ce(23) [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 OOA(8171, 3489, F81, 2, 25) (dual of [(3489, 2), 6907, 26]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8171, 2326, F81, 3, 25) (dual of [(2326, 3), 6907, 26]-NRT-code) | [i] | ||