منابع مشابه
Yet another approach to the extended ternary Golay code
A new proof of the uniqueness and of the existence of the extended ternary Golay code is presented. The proof connects the code to the projective plane of order 3 and is of an elementary nature. The available proofs of the uniqueness of the extended ternary Golay code [2,7] are much more complicated than the standard corresponding proof in the binary case [2]. The prevailing opinion seems to be...
متن کاملThe Tetrahedral Golay Code
Forney conjectured the existence of a “normal realization” (NR) for the [24,12,8] Golay code in which the code appears as a tetrahedron, with 6 output channel bits at each of the 4 vertices and 2 state bits carried by each of the 6 edges. Although the conjecture was dashed by Vardy, we here give a quasi-cyclic NR exhibiting tetrahedral symmetry, confirming the common wisdom that Forney is never...
متن کاملOn the universal embedding of the near hexagon related to the extended ternary Golay code
Let E1 be the near hexagon on 729 points related to the extended ternary Golay code. We prove in an entirely geometricway that the generating and embedding ranks ofE1 are equal to 24. We also study the structure of the universal embeddinge of E1. More precisely, we consider several nice subgeometries A of E1 and determine which kind of embeddingeA is, whereeA is the embedding of A induced by...
متن کاملThe ternary Golay code, the integers mod 9, and the Coxeter-Todd lattice
The 12-dimensional Coxeter-Todd lattice can be obtained by lifting the ternary Golay code to a code over the integers mod 9 and applying Construction A. Several recent papers have pointed out connections between codes over & and lattices [l], [3]. It is the a m of this correspondence to show that the Coxeter-Todd lattice K12 ([4], [5, ch. 4, sec. 91) can be obtained in a similar way from a code...
متن کاملThe Golay Code Outperforms the Extended Golay Code Under Hard-Decision Decoding
We show that the binary Golay code is slightly more power efficient than the extended binary Golay code under maximum-likelihood (ML), hard-decision decoding. In fact, if a codeword from the extended code is transmitted, one cannot achieve a higher probability of correct decoding than by simply ignoring the 24th symbol and using an ML decoder for the non-extended code on the first 23 symbols. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90100-7