Information on Result #1721804
Digital (21, 29, 362)-net over F5, using net defined by OOA based on linear OOA(529, 362, F5, 10, 8) (dual of [(362, 10), 3591, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(529, 725, F5, 2, 8) (dual of [(725, 2), 1421, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(529, 726, F5, 2, 8) (dual of [(726, 2), 1423, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(529, 726, F5, 8) (dual of [726, 697, 9]-code), using
- 90 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 19 times 0, 1, 65 times 0) [i] based on linear OA(525, 632, F5, 8) (dual of [632, 607, 9]-code), using
- construction XX applied to C1 = C([623,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([623,6]) [i] based on
- linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [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(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 = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [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(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
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code) (see above)
- construction XX applied to C1 = C([623,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([623,6]) [i] based on
- 90 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 19 times 0, 1, 65 times 0) [i] based on linear OA(525, 632, F5, 8) (dual of [632, 607, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(529, 726, F5, 8) (dual of [726, 697, 9]-code), using
- discarding factors / shortening the dual code based on linear OOA(529, 726, F5, 2, 8) (dual of [(726, 2), 1423, 9]-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.