MinT - Information on Result #1653294

Information on Result #1653294

Linear OOA(256⁶⁴, 22869, F₂₅₆, 5, 29) (dual of [(22869, 5), 114281, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁴, 22869, F₂₅₆, 2, 29) (dual of [(22869, 2), 45674, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁴, 32780, F₂₅₆, 2, 29) (dual of [(32780, 2), 65496, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁶⁴, 65560, F₂₅₆, 29) (dual of [65560, 65496, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    3. linear OA(256⁷, 23, F₂₅₆, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁷, 256, F₂₅₆, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
        Reedâ€“Solomon code RS(249,256) [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	Linear OOA(256⁶⁴, 7622, F₂₅₆, 35, 29) (dual of [(7622, 35), 266706, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row