Information on Result #1536358
Linear OOA(4122, 46127, F4, 3, 19) (dual of [(46127, 3), 138259, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4122, 46127, F4, 19) (dual of [46127, 46005, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4122, 65563, F4, 19) (dual of [65563, 65441, 20]-code), using
- construction XX applied to C1 = C([0,8]), C2 = C([1,9]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([0,9]) [i] based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(4112, 65537, F4, 10) (dual of [65537, 65425, 11]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,9], and minimum distance d ≥ |{−9,−7,−5,…,9}|+1 = 11 (BCH-bound) [i]
- linear OA(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(496, 65537, F4, 8) (dual of [65537, 65441, 9]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 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
- construction XX applied to C1 = C([0,8]), C2 = C([1,9]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([0,9]) [i] based on
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(4122, 15375, F4, 21, 19) (dual of [(15375, 21), 322753, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |