MinT - Information on Result #1567555

Information on Result #1567555

Linear OOA(256⁵³, 24008, F₂₅₆, 3, 24) (dual of [(24008, 3), 71971, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵³, 24008, F₂₅₆, 2, 24) (dual of [(24008, 2), 47963, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁵³, 32778, F₂₅₆, 2, 24) (dual of [(32778, 2), 65503, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁵³, 65556, F₂₅₆, 24) (dual of [65556, 65503, 25]-code), using
  - constructionÂ X applied to C_e(23) âŠ‚ C_e(16) [i] based on
    1. linear OA(256⁴⁷, 65536, F₂₅₆, 24) (dual of [65536, 65489, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    2. linear OA(256³³, 65536, F₂₅₆, 17) (dual of [65536, 65503, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(256⁵³, 12004, F₂₅₆, 6, 24) (dual of [(12004, 6), 71971, 25]-NRT-code)	[i]		OOA Folding