MinT - Information on Result #1455334

Information on Result #1455334

Linear OOA(16¹²³, 63291, F₁₆, 2, 32) (dual of [(63291, 2), 126459, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16¹²³, 63291, F₁₆, 32) (dual of [63291, 63168, 33]-code), using

discarding factors / shortening the dual code based on linear OA(16¹²³, 65550, F₁₆, 32) (dual of [65550, 65427, 33]-code), using
- 1 times truncation [i] based on linear OA(16¹²⁴, 65551, F₁₆, 33) (dual of [65551, 65427, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(28) [i] based on
    1. linear OA(16¹²¹, 65536, F₁₆, 33) (dual of [65536, 65415, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(16¹⁰⁹, 65536, F₁₆, 29) (dual of [65536, 65427, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(16³, 15, F₁₆, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-cap in PG(2,16)), using
      - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
        Reedâ€“Solomon code RS(13,16) [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(16¹²³, 7911, F₁₆, 34, 32) (dual of [(7911, 34), 268851, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row