MinT - Information on Result #1652911

Information on Result #1652911

Linear OOA(256³⁹, 21949, F₂₅₆, 5, 18) (dual of [(21949, 5), 109706, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256³⁹, 21949, F₂₅₆, 2, 18) (dual of [(21949, 2), 43859, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256³⁹, 32775, F₂₅₆, 2, 18) (dual of [(32775, 2), 65511, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256³⁹, 65550, F₂₅₆, 18) (dual of [65550, 65511, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(12) [i] based on
    1. linear OA(256³⁵, 65536, F₂₅₆, 18) (dual of [65536, 65501, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(256²⁵, 65536, F₂₅₆, 13) (dual of [65536, 65511, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
        Reedâ€“Solomon code RS(252,256) [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(256³⁹, 10974, F₂₅₆, 25, 18) (dual of [(10974, 25), 274311, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row