Information on Result #1539200
Linear OOA(4171, 28791, F4, 3, 29) (dual of [(28791, 3), 86202, 30]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4171, 28791, F4, 2, 29) (dual of [(28791, 2), 57411, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4171, 32773, F4, 2, 29) (dual of [(32773, 2), 65375, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4171, 65546, F4, 29) (dual of [65546, 65375, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4171, 65547, F4, 29) (dual of [65547, 65376, 30]-code), using
- construction XX applied to Ce(28) ⊂ Ce(26) ⊂ Ce(25) [i] based on
- 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(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(41, 10, F4, 1) (dual of [10, 9, 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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(28) ⊂ Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4171, 65547, F4, 29) (dual of [65547, 65376, 30]-code), using
- OOA 2-folding [i] based on linear OA(4171, 65546, F4, 29) (dual of [65546, 65375, 30]-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(4171, 5758, F4, 33, 29) (dual of [(5758, 33), 189843, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |