Information on Result #735583
Linear OA(12870, 16775, F128, 25) (dual of [16775, 16705, 26]-code), using (u, u+v)-construction based on
- linear OA(12820, 385, F128, 12) (dual of [385, 365, 13]-code), using
- construction XX applied to C1 = C([380,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([380,10]) [i] based on
- linear OA(12818, 381, F128, 11) (dual of [381, 363, 12]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12818, 381, F128, 11) (dual of [381, 363, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12820, 381, F128, 12) (dual of [381, 361, 13]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(12816, 381, F128, 10) (dual of [381, 365, 11]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([380,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([380,10]) [i] based on
- linear OA(12850, 16390, F128, 25) (dual of [16390, 16340, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(12845, 16385, F128, 23) (dual of [16385, 16340, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [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(12870, 8387, F128, 2, 25) (dual of [(8387, 2), 16704, 26]-NRT-code) | [i] | OOA Folding | |