Information on Result #686591
Linear OA(8171, 262159, F8, 32) (dual of [262159, 261988, 33]-code), using construction XX applied to Ce(32) ⊂ Ce(29) ⊂ Ce(28) based on
- linear OA(8169, 262144, F8, 33) (dual of [262144, 261975, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(8171, 225510, F8, 2, 32) (dual of [(225510, 2), 450849, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8171, 225510, F8, 3, 32) (dual of [(225510, 3), 676359, 33]-NRT-code) | [i] | ||
| 3 | Digital (139, 171, 225510)-net over F8 | [i] | ||
| 4 | Linear OOA(8171, 131079, F8, 2, 32) (dual of [(131079, 2), 261987, 33]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8171, 87386, F8, 3, 32) (dual of [(87386, 3), 261987, 33]-NRT-code) | [i] | ||