Information on Result #904898
Linear OOA(12864, 5243007, F128, 2, 12) (dual of [(5243007, 2), 10485950, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12819, 1048706, F128, 2, 6) (dual of [(1048706, 2), 2097393, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1283, 129, F128, 2, 3) (dual of [(129, 2), 255, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;255,128) [i]
- linear OOA(12816, 1048577, F128, 2, 6) (dual of [(1048577, 2), 2097138, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12816, 2097154, F128, 6) (dual of [2097154, 2097138, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- OOA 2-folding [i] based on linear OA(12816, 2097154, F128, 6) (dual of [2097154, 2097138, 7]-code), using
- linear OOA(1283, 129, F128, 2, 3) (dual of [(129, 2), 255, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12845, 4194301, F128, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12845, 8388602, F128, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(12845, 8388602, F128, 12) (dual of [8388602, 8388557, 13]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(12864, 2621503, F128, 4, 12) (dual of [(2621503, 4), 10485948, 13]-NRT-code) | [i] | OOA Folding | |