Information on Result #1723491
Linear OOA(5122, 14006, F5, 27, 21) (dual of [(14006, 27), 378040, 22]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(5122, 56025, F5, 3, 21) (dual of [(56025, 3), 167953, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5122, 56026, F5, 3, 21) (dual of [(56026, 3), 167956, 22]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5122, 56026, F5, 21) (dual of [56026, 55904, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(5122, 78153, F5, 21) (dual of [78153, 78031, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(585, 78126, F5, 15) (dual of [78126, 78041, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(59, 27, F5, 5) (dual of [27, 18, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
- linear OA(59, 26, F5, 5) (dual of [26, 17, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(58, 26, F5, 4) (dual of [26, 18, 5]-code), using the narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [1,2], and minimum distance d ≥ |{5,16,1}| + |{−9,−6,−3,0}∖{−3,−9}| = 5 (general Roos-bound) [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(5122, 78153, F5, 21) (dual of [78153, 78031, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5122, 56026, F5, 21) (dual of [56026, 55904, 22]-code), using
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (101, 122, 14006)-net over F5 | [i] | Net Defined by OOA | |