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- W1978603650 abstract "Abstract Let p be a prime, and let ζ p be a primitive p -th root of unity. The lattices in Craig's family are ( p –1)-dimensional and are geometrical representations of the integral ℤ[ζ p ]-ideals 〈1–ζ p 〉 i , where i is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions p – 1 where 149 ≤ p ≤ 3001, Craig's lattices are the densest packings known. Motivated by this, we construct ( p – 1)( q – 1)-dimensional lattices from the integral ℤ[ζ pq ]-ideals 〈1 – ζ p 〉 i 〈1 – ζ q 〉 j , where p and q are distinct primes and i and j are positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties." @default.
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- W1978603650 date "2011-12-01" @default.
- W1978603650 modified "2023-10-03" @default.
- W1978603650 title "An Extension of Craig's Family of Lattices" @default.
- W1978603650 doi "https://doi.org/10.4153/cmb-2011-038-7" @default.
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