MinT - Information on Result #1541373

Information on Result #1541373

Linear OOA(4²⁰¹, 12751, F₄, 3, 37) (dual of [(12751, 3), 38052, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²⁰¹, 12751, F₄, 37) (dual of [12751, 12550, 38]-code), using

discarding factors / shortening the dual code based on linear OA(4²⁰¹, 16423, F₄, 37) (dual of [16423, 16222, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²⁰⁰, 16422, F₄, 37) (dual of [16422, 16222, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(30) [i] based on
    1. linear OA(4¹⁹⁰, 16384, F₄, 37) (dual of [16384, 16194, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    2. linear OA(4¹⁶², 16384, F₄, 31) (dual of [16384, 16222, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. linear OA(4¹⁰, 38, F₄, 5) (dual of [38, 28, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(4²⁰¹, 2125, F₄, 39, 37) (dual of [(2125, 39), 82674, 38]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row