Information on Result #684794
Linear OA(717, 16819, F7, 4) (dual of [16819, 16802, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) based on
- linear OA(716, 16807, F7, 4) (dual of [16807, 16791, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(76, 16807, F7, 2) (dual of [16807, 16801, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(711, 12, F7, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,7)), using
- dual of repetition code with length 12 [i]
- linear OA(71, 12, F7, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
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 OA(718, 16820, F7, 4) (dual of [16820, 16802, 5]-code) | [i] | Code Embedding in Larger Space | |