MinT - Information on Result #735750

Information on Result #735750

Linear OA(128⁴⁵, 16773, F₁₂₈, 16) (dual of [16773, 16728, 17]-code), using (u,Â u+v)-construction based on

linear OA(128¹⁴, 387, F₁₂₈, 8) (dual of [387, 373, 9]-code), using
- (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
  1. linear OA(128², 129, F₁₂₈, 2) (dual of [129, 127, 3]-code or 129-arc in PG(1,128)), using
    - extended Reedâ€“Solomon code RS_e(127,128) [i]
    - Hamming code H(2,128) [i]
  2. linear OA(128⁴, 129, F₁₂₈, 4) (dual of [129, 125, 5]-code or 129-arc in PG(3,128)), using
    - extended Reedâ€“Solomon code RS_e(125,128) [i]
  3. linear OA(128⁸, 129, F₁₂₈, 8) (dual of [129, 121, 9]-code or 129-arc in PG(7,128)), using
    - extended Reedâ€“Solomon code RS_e(121,128) [i]
linear OA(128³¹, 16386, F₁₂₈, 16) (dual of [16386, 16355, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
  1. linear OA(128³¹, 16384, F₁₂₈, 16) (dual of [16384, 16353, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(128²⁹, 16384, F₁₂₈, 15) (dual of [16384, 16355, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  3. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

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:

	Result		This result only	Method
1	Linear OOA(128⁴⁵, 8386, F₁₂₈, 2, 16) (dual of [(8386, 2), 16727, 17]-NRT-code)	[i]		OOA Folding
2	Linear OOA(128⁴⁵, 5591, F₁₂₈, 3, 16) (dual of [(5591, 3), 16728, 17]-NRT-code)	[i]		OOA Folding