Information on Result #732747
Linear OA(25100, 391257, F25, 21) (dual of [391257, 391157, 22]-code), using (u, u+v)-construction based on
- linear OA(2519, 628, F25, 10) (dual of [628, 609, 11]-code), using
- construction XX applied to C1 = C([623,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([623,8]) [i] based on
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([623,8]) [i] based on
- linear OA(2581, 390629, F25, 21) (dual of [390629, 390548, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2577, 390625, F25, 20) (dual of [390625, 390548, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(20) ⊂ Ce(19) [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(25100, 195628, F25, 2, 21) (dual of [(195628, 2), 391156, 22]-NRT-code) | [i] | OOA Folding | |