MinT - Information on Result #1454279

Information on Result #1454279

Linear OOA(16⁹⁴, 124421, F₁₆, 2, 23) (dual of [(124421, 2), 248748, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁹⁴, 124421, F₁₆, 23) (dual of [124421, 124327, 24]-code), using

discarding factors / shortening the dual code based on linear OA(16⁹⁴, 131088, F₁₆, 23) (dual of [131088, 130994, 24]-code), using
- trace code [i] based on linear OA(256⁴⁷, 65544, F₂₅₆, 23) (dual of [65544, 65497, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(19) [i] based on
    1. linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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	Linear OOA(16⁹⁴, 20736, F₁₆, 26, 23) (dual of [(20736, 26), 539042, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row