Information on Result #732665
Linear OA(2588, 16256, F25, 23) (dual of [16256, 16168, 24]-code), using (u, u+v)-construction based on
- linear OA(2521, 628, F25, 11) (dual of [628, 607, 12]-code), using
- construction XX applied to C1 = C([623,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([623,9]) [i] based on
- 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(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [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(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([623,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([623,9]) [i] based on
- linear OA(2567, 15628, F25, 23) (dual of [15628, 15561, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 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(22) ⊂ Ce(21) [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(2588, 8128, F25, 2, 23) (dual of [(8128, 2), 16168, 24]-NRT-code) | [i] | OOA Folding | |