MinT - Information on Result #1615267

Information on Result #1615267

Linear OOA(256¹⁷, 32772, F₂₅₆, 4, 8) (dual of [(32772, 4), 131071, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256¹⁷, 32772, F₂₅₆, 2, 8) (dual of [(32772, 2), 65527, 9]-NRT-code), using

OOA 2-folding [i] based on linear OA(256¹⁷, 65544, F₂₅₆, 8) (dual of [65544, 65527, 9]-code), using
- constructionÂ X applied to C_e(7) âŠ‚ C_e(4) [i] based on
  1. linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  2. linear OA(256⁹, 65536, F₂₅₆, 5) (dual of [65536, 65527, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
  3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
    - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
      - Reedâ€“Solomon code RS(254,256) [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	OOA(128²⁰, 32772, S₁₂₈, 4, 8)	[i]		Discarding Parts of the Base for OOAs
2	Linear OOA(256¹⁷, 32771, F₂₅₆, 5, 8) (dual of [(32771, 5), 163838, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
3	Linear OOA(256¹⁷, 32771, F₂₅₆, 6, 8) (dual of [(32771, 6), 196609, 9]-NRT-code)	[i]
4	Linear OOA(256¹⁷, 32771, F₂₅₆, 12, 8) (dual of [(32771, 12), 393235, 9]-NRT-code)	[i]