Information on Result #1721878
Digital (22, 31, 321)-net over F5, using net defined by OOA based on linear OOA(531, 321, F5, 10, 9) (dual of [(321, 10), 3179, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(531, 643, F5, 2, 9) (dual of [(643, 2), 1255, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(531, 644, F5, 2, 9) (dual of [(644, 2), 1257, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(531, 644, F5, 9) (dual of [644, 613, 10]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(530, 637, F5, 9) (dual of [637, 607, 10]-code), using
- construction XX applied to C1 = C([622,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([622,6]) [i] based on
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(529, 624, F5, 9) (dual of [624, 595, 10]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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 XX applied to C1 = C([622,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([622,6]) [i] based on
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(530, 637, F5, 9) (dual of [637, 607, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(531, 644, F5, 9) (dual of [644, 613, 10]-code), using
- discarding factors / shortening the dual code based on linear OOA(531, 644, F5, 2, 9) (dual of [(644, 2), 1257, 10]-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.