Information on Result #687525
Linear OA(843, 4107, F8, 12) (dual of [4107, 4064, 13]-code), using construction XX applied to Ce(11) ⊂ Ce(9) ⊂ Ce(8) based on
- linear OA(841, 4096, F8, 12) (dual of [4096, 4055, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(833, 4096, F8, 10) (dual of [4096, 4063, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(81, 10, F8, 1) (dual of [10, 9, 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(843, 4011, F8, 2, 12) (dual of [(4011, 2), 7979, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(843, 4011, F8, 3, 12) (dual of [(4011, 3), 11990, 13]-NRT-code) | [i] | ||
| 3 | Digital (31, 43, 4011)-net over F8 | [i] | ||
| 4 | Linear OOA(843, 2053, F8, 2, 12) (dual of [(2053, 2), 4063, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(843, 1369, F8, 3, 12) (dual of [(1369, 3), 4064, 13]-NRT-code) | [i] | ||