Information on Result #1647037
Linear OOA(3186, 22275, F3, 5, 27) (dual of [(22275, 5), 111189, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3186, 22275, F3, 2, 27) (dual of [(22275, 2), 44364, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3186, 29538, F3, 2, 27) (dual of [(29538, 2), 58890, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3186, 59076, F3, 27) (dual of [59076, 58890, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3186, 59077, F3, 27) (dual of [59077, 58891, 28]-code), using
- construction XX applied to Ce(27) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to Ce(27) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3186, 59077, F3, 27) (dual of [59077, 58891, 28]-code), using
- OOA 2-folding [i] based on linear OA(3186, 59076, F3, 27) (dual of [59076, 58890, 28]-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(3186, 7424, F3, 35, 27) (dual of [(7424, 35), 259654, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |