Information on Result #686600
Linear OA(8142, 262160, F8, 27) (dual of [262160, 262018, 28]-code), using construction XX applied to Ce(26) ⊂ Ce(24) ⊂ Ce(22) based on
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 14, F8, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(8142, 180268, F8, 2, 27) (dual of [(180268, 2), 360394, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8142, 180268, F8, 3, 27) (dual of [(180268, 3), 540662, 28]-NRT-code) | [i] | ||
| 3 | Digital (115, 142, 180268)-net over F8 | [i] | ||
| 4 | Linear OOA(8142, 131080, F8, 2, 27) (dual of [(131080, 2), 262018, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8142, 20166, F8, 27, 27) (dual of [(20166, 27), 544340, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |