MinT - Information on Result #903535

Information on Result #903535

Linear OOA(64¹⁶, 135234, F₆₄, 2, 5) (dual of [(135234, 2), 270452, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64³, 4161, F₆₄, 2, 2) (dual of [(4161, 2), 8319, 3]-NRT-code), using
- appending kth column [i] based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
  - Hamming code H(3,64) [i]
linear OOA(64¹³, 131073, F₆₄, 2, 5) (dual of [(131073, 2), 262133, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64¹³, 262146, F₆₄, 5) (dual of [262146, 262133, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(64¹³, 262147, F₆₄, 5) (dual of [262147, 262134, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(64¹³, 262144, F₆₄, 5) (dual of [262144, 262131, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(64¹⁰, 262144, F₆₄, 4) (dual of [262144, 262134, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁵³, 4329535, F₆₄, 2, 10) (dual of [(4329535, 2), 8659017, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵⁷, 4329535, F₆₄, 2, 11) (dual of [(4329535, 2), 8659013, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs