Information on Result #1537807
Linear OOA(4149, 31794, F4, 3, 25) (dual of [(31794, 3), 95233, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4149, 31794, F4, 2, 25) (dual of [(31794, 2), 63439, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4149, 32778, F4, 2, 25) (dual of [(32778, 2), 65407, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4149, 65556, F4, 25) (dual of [65556, 65407, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(43, 20, F4, 2) (dual of [20, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code), using
- OOA 2-folding [i] based on linear OA(4149, 65556, F4, 25) (dual of [65556, 65407, 26]-code), using
Mode: 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(4149, 7948, F4, 27, 25) (dual of [(7948, 27), 214447, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |