MinT - Information on Result #1455465

Information on Result #1455465

Linear OOA(16¹²⁶, 120545, F₁₆, 2, 31) (dual of [(120545, 2), 240964, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16¹²⁶, 120545, F₁₆, 31) (dual of [120545, 120419, 32]-code), using

discarding factors / shortening the dual code based on linear OA(16¹²⁶, 131088, F₁₆, 31) (dual of [131088, 130962, 32]-code), using
- trace code [i] based on linear OA(256⁶³, 65544, F₂₅₆, 31) (dual of [65544, 65481, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [i] based on
    1. linear OA(256⁶¹, 65536, F₂₅₆, 31) (dual of [65536, 65475, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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(16¹²⁶, 15068, F₁₆, 34, 31) (dual of [(15068, 34), 512186, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row