MinT - Information on Result #1614233

Information on Result #1614233

Linear OOA(81⁸¹, 234611, F₈₁, 4, 27) (dual of [(234611, 4), 938363, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁸¹, 234611, F₈₁, 2, 27) (dual of [(234611, 2), 469141, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁸¹, 265726, F₈₁, 2, 27) (dual of [(265726, 2), 531371, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁸¹, 531452, F₈₁, 27) (dual of [531452, 531371, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(23) [i] based on
    1. linear OA(81⁷⁹, 531441, F₈₁, 27) (dual of [531441, 531362, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(81⁷⁰, 531441, F₈₁, 24) (dual of [531441, 531371, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    3. linear OA(81², 11, F₈₁, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,81)), using
      - discarding factors / shortening the dual code based on linear OA(81², 81, F₈₁, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
        Reedâ€“Solomon code RS(79,81) [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(81⁸¹, 58652, F₈₁, 36, 27) (dual of [(58652, 36), 2111391, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row