MinT - Information on Result #878465

Information on Result #878465

Linear OOA(128⁴³, 1048583, F₁₂₈, 2, 14) (dual of [(1048583, 2), 2097123, 15]-NRT-code), using OOA 2-folding based on linear OA(128⁴³, 2097166, F₁₂₈, 14) (dual of [2097166, 2097123, 15]-code), using

discarding factors / shortening the dual code based on linear OA(128⁴³, 2097167, F₁₂₈, 14) (dual of [2097167, 2097124, 15]-code), using
- constructionÂ X applied to C_e(13) âŠ‚ C_e(9) [i] based on
  1. linear OA(128⁴⁰, 2097152, F₁₂₈, 14) (dual of [2097152, 2097112, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  2. linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(128³, 15, F₁₂₈, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-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(128⁴³, 1048583, F₁₂₈, 3, 14) (dual of [(1048583, 3), 3145706, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(128⁴³, 1048583, F₁₂₈, 4, 14) (dual of [(1048583, 4), 4194289, 15]-NRT-code)	[i]
3	Digital (29, 43, 1048583)-net over F₁₂₈	[i]