Information on Result #1541063
Linear OOA(4197, 32778, F4, 3, 33) (dual of [(32778, 3), 98137, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4197, 32778, F4, 2, 33) (dual of [(32778, 2), 65359, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4197, 65556, F4, 33) (dual of [65556, 65359, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4197, 65557, F4, 33) (dual of [65557, 65360, 34]-code), using
- construction XX applied to Ce(32) ⊂ Ce(29) ⊂ Ce(28) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(32) ⊂ Ce(29) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4197, 65557, F4, 33) (dual of [65557, 65360, 34]-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(4197, 5462, F4, 39, 33) (dual of [(5462, 39), 212821, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |