MinT - Information on Result #1453793

Information on Result #1453793

Linear OOA(16⁷⁶, 52376, F₁₆, 2, 20) (dual of [(52376, 2), 104676, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁷⁶, 52376, F₁₆, 20) (dual of [52376, 52300, 21]-code), using

discarding factors / shortening the dual code based on linear OA(16⁷⁶, 65551, F₁₆, 20) (dual of [65551, 65475, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁷⁵, 65550, F₁₆, 20) (dual of [65550, 65475, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(16) [i] based on
    1. linear OA(16⁷³, 65536, F₁₆, 20) (dual of [65536, 65463, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(16⁶¹, 65536, F₁₆, 17) (dual of [65536, 65475, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(16², 14, F₁₆, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
      - discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [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(16⁷⁶, 10475, F₁₆, 22, 20) (dual of [(10475, 22), 230374, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row