MinT - Information on Result #1567356

Information on Result #1567356

Linear OOA(256³⁵, 28841, F₂₅₆, 3, 16) (dual of [(28841, 3), 86488, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256³⁵, 28841, F₂₅₆, 2, 16) (dual of [(28841, 2), 57647, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256³⁵, 32775, F₂₅₆, 2, 16) (dual of [(32775, 2), 65515, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256³⁵, 65550, F₂₅₆, 16) (dual of [65550, 65515, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
    1. 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]
    2. linear OA(256²¹, 65536, F₂₅₆, 11) (dual of [65536, 65515, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
        Reedâ€“Solomon code RS(252,256) [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(256³⁵, 14420, F₂₅₆, 5, 16) (dual of [(14420, 5), 72065, 17]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256³⁵, 14420, F₂₅₆, 6, 16) (dual of [(14420, 6), 86485, 17]-NRT-code)	[i]		OOA Folding