Information on Result #1485166
Linear OOA(559, 285, F5, 3, 18) (dual of [(285, 3), 796, 19]-NRT-code), using OOA 2-folding based on linear OOA(559, 570, F5, 2, 18) (dual of [(570, 2), 1081, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(559, 571, F5, 2, 18) (dual of [(571, 2), 1083, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(559, 571, F5, 18) (dual of [571, 512, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(559, 638, F5, 18) (dual of [638, 579, 19]-code), using
- construction XX applied to C1 = C([622,13]), C2 = C([0,15]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([622,15]) [i] based on
- linear OA(553, 624, F5, 16) (dual of [624, 571, 17]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,13}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(549, 624, F5, 16) (dual of [624, 575, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,15}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- construction XX applied to C1 = C([622,13]), C2 = C([0,15]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([622,15]) [i] based on
- discarding factors / shortening the dual code based on linear OA(559, 638, F5, 18) (dual of [638, 579, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(559, 571, F5, 18) (dual of [571, 512, 19]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.