MinT - Information on Result #1017778

Information on Result #1017778

Linear OOA(64³⁴, 1496, F₆₄, 3, 13) (dual of [(1496, 3), 4454, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64⁹, 130, F₆₄, 3, 6) (dual of [(130, 3), 381, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64³, 65, F₆₄, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;192,64) [i]
  2. linear OOA(64⁶, 65, F₆₄, 3, 6) (dual of [(65, 3), 189, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;189,64) [i]
linear OOA(64²⁵, 1366, F₆₄, 3, 13) (dual of [(1366, 3), 4073, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64²⁵, 4098, F₆₄, 13) (dual of [4098, 4073, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
    1. linear OA(64²⁵, 4096, F₆₄, 13) (dual of [4096, 4071, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(64²³, 4096, F₆₄, 12) (dual of [4096, 4073, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and 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(64³⁴, 747, F₆₄, 15, 13) (dual of [(747, 15), 11171, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row