MinT - Information on Result #1615175

Information on Result #1615175

Linear OOA(128⁷⁶, 5490, F₁₂₈, 4, 36) (dual of [(5490, 4), 21884, 37]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁷⁶, 5490, F₁₂₈, 2, 36) (dual of [(5490, 2), 10904, 37]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁷⁶, 8200, F₁₂₈, 2, 36) (dual of [(8200, 2), 16324, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁷⁶, 16400, F₁₂₈, 36) (dual of [16400, 16324, 37]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁷⁶, 16401, F₁₂₈, 36) (dual of [16401, 16325, 37]-code), using
    - constructionÂ X applied to C_e(35) âŠ‚ C_e(29) [i] based on
      1. linear OA(128⁷¹, 16384, F₁₂₈, 36) (dual of [16384, 16313, 37]-code), using an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
      2. linear OA(128⁵⁹, 16384, F₁₂₈, 30) (dual of [16384, 16325, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      3. linear OA(128⁵, 17, F₁₂₈, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [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(128⁷⁶, 1097, F₁₂₈, 44, 36) (dual of [(1097, 44), 48192, 37]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row