Information on Result #687419
Linear OA(8163, 4107, F8, 46) (dual of [4107, 3944, 47]-code), using construction XX applied to Ce(45) ⊂ Ce(43) ⊂ Ce(42) based on
- linear OA(8161, 4096, F8, 46) (dual of [4096, 3935, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(8153, 4096, F8, 44) (dual of [4096, 3943, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(8149, 4096, F8, 43) (dual of [4096, 3947, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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(8163, 2053, F8, 2, 46) (dual of [(2053, 2), 3943, 47]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8163, 1369, F8, 3, 46) (dual of [(1369, 3), 3944, 47]-NRT-code) | [i] | ||