MinT - Information on Result #1565143

Information on Result #1565143

Linear OOA(64⁸⁴, 131077, F₆₄, 3, 28) (dual of [(131077, 3), 393147, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁸⁴, 131077, F₆₄, 2, 28) (dual of [(131077, 2), 262070, 29]-NRT-code), using

OOA 2-folding [i] based on linear OA(64⁸⁴, 262154, F₆₄, 28) (dual of [262154, 262070, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁸⁴, 262155, F₆₄, 28) (dual of [262155, 262071, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(24) [i] based on
    1. linear OA(64⁸², 262144, F₆₄, 28) (dual of [262144, 262062, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(64⁷³, 262144, F₆₄, 25) (dual of [262144, 262071, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(64², 11, F₆₄, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
      - discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [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(64⁸⁴, 26215, F₆₄, 33, 28) (dual of [(26215, 33), 865011, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row