Information on Result #1307944
Linear OA(4103, 1085, F4, 26) (dual of [1085, 982, 27]-code), using 45 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0) based on linear OA(497, 1034, F4, 26) (dual of [1034, 937, 27]-code), using
- construction XX applied to C1 = C([317,341]), C2 = C([319,342]), C3 = C1 + C2 = C([319,341]), and C∩ = C1 ∩ C2 = C([317,342]) [i] based on
- linear OA(491, 1023, F4, 25) (dual of [1023, 932, 26]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {317,318,…,341}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 1023, F4, 24) (dual of [1023, 932, 25]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {319,320,…,342}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {317,318,…,342}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(486, 1023, F4, 23) (dual of [1023, 937, 24]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {319,320,…,341}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 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, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(4103, 1085, F4, 2, 26) (dual of [(1085, 2), 2067, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4103, 1085, F4, 3, 26) (dual of [(1085, 3), 3152, 27]-NRT-code) | [i] | ||
| 3 | Digital (77, 103, 1085)-net over F4 | [i] | ||
| 4 | Linear OOA(4103, 542, F4, 2, 26) (dual of [(542, 2), 981, 27]-NRT-code) | [i] | OOA Folding | |