MinT - Information on Result #878520

Information on Result #878520

Linear OOA(128³⁴, 8197, F₁₂₈, 2, 16) (dual of [(8197, 2), 16360, 17]-NRT-code), using OOA 2-folding based on linear OA(128³⁴, 16394, F₁₂₈, 16) (dual of [16394, 16360, 17]-code), using

discarding factors / shortening the dual code based on linear OA(128³⁴, 16395, F₁₂₈, 16) (dual of [16395, 16361, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(11) [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(128²³, 16384, F₁₂₈, 12) (dual of [16384, 16361, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  3. linear OA(128³, 11, F₁₂₈, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
    - discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
      - Reedâ€“Solomon code RS(125,128) [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		Method
1	Linear OOA(128³⁴, 6858, F₁₂₈, 3, 16) (dual of [(6858, 3), 20540, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(128³⁴, 6858, F₁₂₈, 4, 16) (dual of [(6858, 4), 27398, 17]-NRT-code)	[i]
3	Digital (18, 34, 6858)-net over F₁₂₈	[i]