Information on Result #1019227
Linear OOA(12841, 699201, F128, 3, 12) (dual of [(699201, 3), 2097562, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1287, 150, F128, 3, 6) (dual of [(150, 3), 443, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,443P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12834, 699051, F128, 3, 12) (dual of [(699051, 3), 2097119, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12834, 2097153, F128, 12) (dual of [2097153, 2097119, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- OOA 3-folding [i] based on linear OA(12834, 2097153, F128, 12) (dual of [2097153, 2097119, 13]-code), using
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(12841, 349600, F128, 15, 12) (dual of [(349600, 15), 5243959, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |