MinT - Information on Result #1567695

Information on Result #1567695

Linear OOA(256⁶³, 29993, F₂₅₆, 3, 28) (dual of [(29993, 3), 89916, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶³, 29993, F₂₅₆, 2, 28) (dual of [(29993, 2), 59923, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶³, 32781, F₂₅₆, 2, 28) (dual of [(32781, 2), 65499, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁶³, 65562, F₂₅₆, 28) (dual of [65562, 65499, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(18) [i] based on
    1. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(256³⁷, 65536, F₂₅₆, 19) (dual of [65536, 65499, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(256⁸, 26, F₂₅₆, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁸, 256, F₂₅₆, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
        Reedâ€“Solomon code RS(248,256) [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(256⁶³, 14996, F₂₅₆, 5, 28) (dual of [(14996, 5), 74917, 29]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256⁶³, 14996, F₂₅₆, 6, 28) (dual of [(14996, 6), 89913, 29]-NRT-code)	[i]		OOA Folding