Information on Result #1530442
Linear OOA(3223, 4194362, F3, 3, 20) (dual of [(4194362, 3), 12582863, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3223, 4194362, F3, 2, 20) (dual of [(4194362, 2), 8388501, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(327, 61, F3, 2, 10) (dual of [(61, 2), 95, 11]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(327, 61, F3, 10) (dual of [61, 34, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(327, 88, F3, 10) (dual of [88, 61, 11]-code), using
- construction XX applied to Ce(9) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- linear OA(325, 81, F3, 10) (dual of [81, 56, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(321, 81, F3, 8) (dual of [81, 60, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(317, 81, F3, 7) (dual of [81, 64, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(9) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(327, 88, F3, 10) (dual of [88, 61, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(327, 61, F3, 10) (dual of [61, 34, 11]-code), using
- linear OOA(3196, 4194301, F3, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- linear OOA(327, 61, F3, 2, 10) (dual of [(61, 2), 95, 11]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3223, 2097181, F3, 5, 20) (dual of [(2097181, 5), 10485682, 21]-NRT-code) | [i] | OOA Folding | |