Information on Result #895519
Linear OOA(4126, 4194431, F4, 2, 13) (dual of [(4194431, 2), 8388736, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(417, 130, F4, 2, 6) (dual of [(130, 2), 243, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(417, 260, F4, 6) (dual of [260, 243, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(417, 256, F4, 6) (dual of [256, 239, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(413, 256, F4, 5) (dual of [256, 243, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OOA 2-folding [i] based on linear OA(417, 260, F4, 6) (dual of [260, 243, 7]-code), using
- linear OOA(4109, 4194301, F4, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-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(4126, 1398143, F4, 14, 13) (dual of [(1398143, 14), 19573876, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |