Information on Result #711997

Linear OA(5103, 632, F5, 33) (dual of [632, 529, 34]-code), using construction XX applied to C1 = C([623,30]), C2 = C([0,31]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([623,31]) based on
  1. linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [i]
  2. linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
  3. linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
  4. linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
  5. linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
  6. linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code) (see above)

Mode: Constructive and 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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(5104, 637, F5, 33) (dual of [637, 533, 34]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(5105, 652, F5, 33) (dual of [652, 547, 34]-code) [i]
3Linear OA(5106, 679, F5, 33) (dual of [679, 573, 34]-code) [i]
4Linear OOA(5103, 316, F5, 2, 33) (dual of [(316, 2), 529, 34]-NRT-code) [i]OOA Folding
5Linear OOA(5103, 210, F5, 3, 33) (dual of [(210, 3), 527, 34]-NRT-code) [i]