MinT - Information on Result #1567504

Information on Result #1567504

Linear OOA(256⁴⁹, 28169, F₂₅₆, 3, 22) (dual of [(28169, 3), 84458, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁴⁹, 28169, F₂₅₆, 2, 22) (dual of [(28169, 2), 56289, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁴⁹, 32778, F₂₅₆, 2, 22) (dual of [(32778, 2), 65507, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁴⁹, 65556, F₂₅₆, 22) (dual of [65556, 65507, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(14) [i] based on
    1. linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(256²⁹, 65536, F₂₅₆, 15) (dual of [65536, 65507, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(256⁶, 20, F₂₅₆, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁶, 256, F₂₅₆, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
        Reedâ€“Solomon code RS(250,256) [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(256⁴⁹, 14084, F₂₅₆, 5, 22) (dual of [(14084, 5), 70371, 23]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256⁴⁹, 14084, F₂₅₆, 6, 22) (dual of [(14084, 6), 84455, 23]-NRT-code)	[i]		OOA Folding