Information on Result #1723428
Digital (66, 87, 719)-net over F5, using net defined by OOA based on linear OOA(587, 719, F5, 27, 21) (dual of [(719, 27), 19326, 22]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(587, 2877, F5, 3, 21) (dual of [(2877, 3), 8544, 22]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(587, 2877, F5, 21) (dual of [2877, 2790, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(587, 3148, F5, 21) (dual of [3148, 3061, 22]-code), using
- construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(15) [i] based on
- linear OA(581, 3125, F5, 21) (dual of [3125, 3044, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(566, 3125, F5, 17) (dual of [3125, 3059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(561, 3125, F5, 16) (dual of [3125, 3064, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(54, 21, F5, 3) (dual of [21, 17, 4]-code or 21-cap in PG(3,5)), using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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 Ce(20) ⊂ Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(587, 3148, F5, 21) (dual of [3148, 3061, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(587, 2877, F5, 21) (dual of [2877, 2790, 22]-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.