Information on Result #895553
Linear OOA(4153, 4196356, F4, 2, 14) (dual of [(4196356, 2), 8392559, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(432, 2055, F4, 2, 7) (dual of [(2055, 2), 4078, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(432, 4110, F4, 7) (dual of [4110, 4078, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(431, 4096, F4, 7) (dual of [4096, 4065, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(419, 4096, F4, 5) (dual of [4096, 4077, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- dual of repetition code with length 14 [i]
- linear OA(41, 14, F4, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- OOA 2-folding [i] based on linear OA(432, 4110, F4, 7) (dual of [4110, 4078, 8]-code), using
- linear OOA(4121, 4194301, F4, 2, 14) (dual of [(4194301, 2), 8388481, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4121, 8388602, F4, 14) (dual of [8388602, 8388481, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- OOA 2-folding [i] based on linear OA(4121, 8388602, F4, 14) (dual of [8388602, 8388481, 15]-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(4155, 4196357, F4, 2, 14) (dual of [(4196357, 2), 8392559, 15]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4154, 4196356, F4, 2, 14) (dual of [(4196356, 2), 8392558, 15]-NRT-code) | [i] | OOA Duplication | |