Information on Result #1421877
Linear OOA(4112, 12979, F4, 2, 20) (dual of [(12979, 2), 25846, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4112, 12979, F4, 20) (dual of [12979, 12867, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4112, 16412, F4, 20) (dual of [16412, 16300, 21]-code), using
- 1 times truncation [i] based on linear OA(4113, 16413, F4, 21) (dual of [16413, 16300, 22]-code), using
- construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(4113, 16413, F4, 21) (dual of [16413, 16300, 22]-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(4112, 6489, F4, 3, 20) (dual of [(6489, 3), 19355, 21]-NRT-code) | [i] | OOA Folding | |