MinT - Information on Result #1537065

Information on Result #1537065

Linear OOA(4¹³⁶, 511727, F₄, 3, 18) (dual of [(511727, 3), 1535045, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹³⁶, 511727, F₄, 2, 18) (dual of [(511727, 2), 1023318, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹³⁶, 524305, F₄, 2, 18) (dual of [(524305, 2), 1048474, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹³⁶, 1048610, F₄, 18) (dual of [1048610, 1048474, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³⁶, 1048611, F₄, 18) (dual of [1048611, 1048475, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(13) [i] based on
      1. linear OA(4¹³¹, 1048576, F₄, 18) (dual of [1048576, 1048445, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(4¹⁰¹, 1048576, F₄, 14) (dual of [1048576, 1048475, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(4⁵, 35, F₄, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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(4¹³⁶, 170575, F₄, 21, 18) (dual of [(170575, 21), 3581939, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row