A new upper bound for the minimum of an integral lattice of determinant 1

DOI10.1090/S0273-0979-1990-15940-3zbMath0709.11030OpenAlexW2127123421MaRDI QIDQ3491659

N. J. A. Sloane, Conway, John H.

Publication date: 1990

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1990-15940-3

zbMATH Keywords

theta seriesself-dual codesminimal squared lengthn-dimensional integral lattice

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Class numbers of quadratic and Hermitian forms (11E41)

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Modular lattices from a variation of construction A over number fields, Automorphisms of extremal unimodular lattices in dimension 72, Fermionic CFTs from classical codes over finite fields, Splitting the shadow., An optimal odd unimodular lattice in dimension 72, A shadow identity and an application to isoduality., A complete classification of ternary self-dual codes of length 24, A note on optimal unimodular lattices, The shadow theory of modular and unimodular lattices, Construction of new extremal unimodular lattices

Cites Work

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• On the enumeration of self-dual codes
• Upper bounds for modular forms, lattices, and codes
• The Leech lattice
• New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
• Extremal self‐dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24
• An upper bound for self-dual codes