On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7

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.

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

ACM Computing Classification System (1998): E.4.

Large Distinct Part Sizes in a Random Integer Partition

A partition of a positive integer n is a way of writing it as the sum of positive integers without regard to order; the summands are called parts. The number of partitions of n, usually denoted by p(n), is determined asymptotically by the famous partition formula of Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P on the set of all partitions of n assuming that the probability 1/p(n) is assigned to each n-partition. The symbols E and V ar will be further used to denote the expectation and variance with respect to the measure P . Thus, each conceivable numerical characteristic of the parts in a partition can be regarded as a random variable.

Constructing 7-Clusters

ACM Computing Classification System (1998): G.2, G.4.

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.

New Coefficient Conditions for Functions Starlike with Respect to Symmetric Points

2000 Mathematics Subject Classification: Primary 30C45, secondary 30C80.

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

On strongly regular graphs with m2 = qm3 and m3 = qm2

2010 Mathematics Subject Classification: 05C50.