MinT - Information on Result #1673011

Information on Result #1673011

Linear OOA(256⁵⁴, 31267, F₂₅₆, 6, 24) (dual of [(31267, 6), 187548, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵⁴, 31267, F₂₅₆, 2, 24) (dual of [(31267, 2), 62480, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁵⁴, 32779, F₂₅₆, 2, 24) (dual of [(32779, 2), 65504, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁵⁴, 65558, F₂₅₆, 24) (dual of [65558, 65504, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁵⁴, 65559, F₂₅₆, 24) (dual of [65559, 65505, 25]-code), using
    - constructionÂ X applied to C_e(23) âŠ‚ C_e(15) [i] based on
      1. linear OA(256⁴⁷, 65536, F₂₅₆, 24) (dual of [65536, 65489, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
      2. linear OA(256³¹, 65536, F₂₅₆, 16) (dual of [65536, 65505, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(256⁵⁴, 15633, F₂₅₆, 30, 24) (dual of [(15633, 30), 468936, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row