Information on Result #1723492
Digital (101, 122, 14006)-net over F5, using net defined by OOA based on linear OOA(5122, 14006, F5, 27, 21) (dual of [(14006, 27), 378040, 22]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] 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
- discarding factors / shortening the dual code based on linear OOA(5122, 56026, F5, 3, 21) (dual of [(56026, 3), 167956, 22]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.