Information on Result #679277
Linear OA(4249, 16402, F4, 47) (dual of [16402, 16153, 48]-code), using construction XX applied to Ce(46) ⊂ Ce(44) ⊂ Ce(42) based on
- linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4225, 16384, F4, 43) (dual of [16384, 16159, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(41, 16, F4, 1) (dual of [16, 15, 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
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(4249, 12184, F4, 2, 47) (dual of [(12184, 2), 24119, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4249, 12184, F4, 3, 47) (dual of [(12184, 3), 36303, 48]-NRT-code) | [i] | ||
| 3 | Digital (202, 249, 12184)-net over F4 | [i] | ||
| 4 | Linear OOA(4249, 8201, F4, 2, 47) (dual of [(8201, 2), 16153, 48]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4249, 5467, F4, 3, 47) (dual of [(5467, 3), 16152, 48]-NRT-code) | [i] | ||