MinT - Information on Result #878812

Information on Result #878812

Linear OOA(128⁶⁸, 1048585, F₁₂₈, 2, 22) (dual of [(1048585, 2), 2097102, 23]-NRT-code), using OOA 2-folding based on linear OA(128⁶⁸, 2097170, F₁₂₈, 22) (dual of [2097170, 2097102, 23]-code), using

discarding factors / shortening the dual code based on linear OA(128⁶⁸, 2097171, F₁₂₈, 22) (dual of [2097171, 2097103, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
  1. linear OA(128⁶⁴, 2097152, F₁₂₈, 22) (dual of [2097152, 2097088, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  2. linear OA(128⁴⁹, 2097152, F₁₂₈, 17) (dual of [2097152, 2097103, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(128⁴, 19, F₁₂₈, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
    - discarding factors / shortening the dual code based on linear OA(128⁴, 128, F₁₂₈, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
      - Reedâ€“Solomon code RS(124,128) [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(128⁶⁸, 1048585, F₁₂₈, 3, 22) (dual of [(1048585, 3), 3145687, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(128⁶⁸, 1048585, F₁₂₈, 4, 22) (dual of [(1048585, 4), 4194272, 23]-NRT-code)	[i]
3	Digital (46, 68, 1048585)-net over F₁₂₈	[i]