Information on Result #1305300
Linear OA(3231, 3296, F3, 44) (dual of [3296, 3065, 45]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(3230, 3291, F3, 44) (dual of [3291, 3061, 45]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3229, 3289, F3, 44) (dual of [3289, 3060, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(42) [i] based on
- linear OA(3229, 3281, F3, 44) (dual of [3281, 3052, 45]-code), using an extension Ce(43) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using an extension Ce(42) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(43) ⊂ Ce(42) [i] based on
- linear OA(3229, 3290, F3, 43) (dual of [3290, 3061, 44]-code), using Gilbert–Varšamov bound and bm = 3229 > Vbs−1(k−1) = 12 615641 539872 118256 399378 807082 663458 339630 606048 599909 154946 097516 291712 410334 781485 058789 550974 366987 878307 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- linear OA(3229, 3289, F3, 44) (dual of [3289, 3060, 45]-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(3231, 3296, F3, 2, 44) (dual of [(3296, 2), 6361, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3231, 3296, F3, 3, 44) (dual of [(3296, 3), 9657, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3231, 3296, F3, 4, 44) (dual of [(3296, 4), 12953, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(3231, 3296, F3, 5, 44) (dual of [(3296, 5), 16249, 45]-NRT-code) | [i] | ||
| 5 | Digital (187, 231, 3296)-net over F3 | [i] | ||
| 6 | Linear OOA(3231, 1648, F3, 2, 44) (dual of [(1648, 2), 3065, 45]-NRT-code) | [i] | OOA Folding | |