MinT - Information on Result #1567284

Information on Result #1567284

Linear OOA(256²⁵, 23203, F₂₅₆, 3, 12) (dual of [(23203, 3), 69584, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256²⁵, 23203, F₂₅₆, 2, 12) (dual of [(23203, 2), 46381, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256²⁵, 32772, F₂₅₆, 2, 12) (dual of [(32772, 2), 65519, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256²⁵, 65544, F₂₅₆, 12) (dual of [65544, 65519, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(8) [i] based on
    1. linear OA(256²³, 65536, F₂₅₆, 12) (dual of [65536, 65513, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(256¹⁷, 65536, F₂₅₆, 9) (dual of [65536, 65519, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(128²⁹, 23203, S₁₂₈, 3, 12)	[i]		Discarding Parts of the Base for OOAs
2	Linear OOA(256²⁵, 11601, F₂₅₆, 6, 12) (dual of [(11601, 6), 69581, 13]-NRT-code)	[i]		OOA Folding