MinT - Information on Result #1566477

Information on Result #1566477

Linear OOA(128³², 7714, F₁₂₈, 3, 15) (dual of [(7714, 3), 23110, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128³², 7714, F₁₂₈, 2, 15) (dual of [(7714, 2), 15396, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128³², 8198, F₁₂₈, 2, 15) (dual of [(8198, 2), 16364, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128³², 16396, F₁₂₈, 15) (dual of [16396, 16364, 16]-code), using
  - constructionÂ X applied to C([0,7]) âŠ‚ C([0,5]) [i] based on
    1. linear OA(128²⁹, 16385, F₁₂₈, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    2. linear OA(128²¹, 16385, F₁₂₈, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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: 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	OOA(64³⁸, 7714, S₆₄, 3, 15)	[i]		Discarding Parts of the Base for OOAs