Information on Result #732831
Linear OA(2578, 390709, F25, 17) (dual of [390709, 390631, 18]-code), using (u, u+v)-construction based on
- linear OA(2513, 80, F25, 8) (dual of [80, 67, 9]-code), using
- construction X applied to C([9,16]) ⊂ C([10,16]) [i] based on
- linear OA(2513, 78, F25, 8) (dual of [78, 65, 9]-code), using the BCH-code C(I) with length 78 | 252−1, defining interval I = {9,10,…,16}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2511, 78, F25, 7) (dual of [78, 67, 8]-code), using the BCH-code C(I) with length 78 | 252−1, defining interval I = {10,11,…,16}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([9,16]) ⊂ C([10,16]) [i] based on
- linear OA(2565, 390629, F25, 17) (dual of [390629, 390564, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
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(2578, 195354, F25, 2, 17) (dual of [(195354, 2), 390630, 18]-NRT-code) | [i] | OOA Folding | |