Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)

Eiichi Bannai

Displaying similar documents to “Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)”

What is Q-extension?

Bouyukliev, Iliya (2007)

Serdica Journal of Computing

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In this paper we present a developed software in the area of Coding Theory. Using it, codes with given properties can be classified. A part of this software can be used also for investigations (isomorphisms, automorphism groups) of other discrete structures-combinatorial designs, Hadamard matrices, bipartite graphs etc.

On the topography of Maass waveforms for $PSL (2, ℤ)$ .

Hejhal, Dennis A., Rackner, Barry N. (1992)

Experimental Mathematics

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New Binary Extremal Self-Dual Codes of Lengths 50 and 52

Buyuklieva, Stefka (1999)

Serdica Mathematical Journal

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* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995. New extremal binary self-dual codes of lengths 50 and 52 are constructed. Some of them are the first known codes with such weight enumerators. The structure of their automorphisms groups are shown.

$2$ -modular lattices from ternary codes

Robin Chapman, Steven T. Dougherty, Philippe Gaborit, Patrick Solé (2002)

Journal de théorie des nombres de Bordeaux

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The alphabet $𝐅_{3} + v 𝐅_{3}$ where $v^{2} = 1$ is viewed here as a quotient of the ring of integers of $𝐐 (\sqrt{- 2})$ by the ideal (3). Self-dual $𝐅_{3} + v 𝐅_{3}$ codes for the hermitian scalar product give $2$ -modular lattices by construction $A_{K}$ . There is a Gray map which maps self-dual codes for the Euclidean scalar product into Type III codes with a fixed point free involution in their automorphism group. Gleason type theorems for the symmetrized weight enumerators of Euclidean self-dual codes and the length weight enumerator of hermitian...

On $7$ - and $8$ -decomposable finite groups

Ali Reza Ashrafi, Wu Jie Shi (2005)

Mathematica Slovaca

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Synthesis of finite state machines for CPLDs

Robert Czerwiński, Dariusz Kania (2009)

International Journal of Applied Mathematics and Computer Science

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The paper presents a new two-step approach to FSM synthesis for PAL-based CPLDs that strives to find an optimum fit of an FSM to the structure of the CPLD. The first step, the original state assignment method, includes techniques of twolevel minimization and aims at area minimization. The second step, PAL-oriented multi-level optimization, is a search for implicants that can be shared by several functions. It is based on the graph of outputs. Results of experiments prove that the presented...

CAPS in Z(2,n)

Kurz, Sascha (2009)

Serdica Journal of Computing

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We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7 Двоични самодуални кодове с дължина 62 притежаващи автоморфизъм от ред 7

Yankov, Nikolay (2011)

Union of Bulgarian Mathematicians

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Николай Янков - Класифицирани са с точност до еквивалетност всички оптимални двоични самодуални [62, 31, 12] кодове, които притежават автоморфизъм от ред 7 с 8 независими цикъла при разлагане на независими цикли. Използвайки метода за конструиране на самодуални кодове, притежаващи автоморфизъм от нечетен прост ред е доказано, че съществуват точно 8 нееквивалентни такива кода. Три от получените кодове имат тегловна функция, каквато досега не бе известно да съществува. We...