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Nikolay Yankov

Publications and source records attributed to Nikolay Yankov.

6 recordsLinked to original sources
arXiv2018

A note on reducing the computation time for minimum distance and equivalence check of binary linear codes

In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have also considered the usefulness of combinatorial $2$-$(t,k,1)$ designs when there are memory limitations to the number of objects (linear codes in particular) that can be tested for equivalence.

cs.IT↗
arXiv2017

Classification of binary self-dual [76, 38, 14] codes with an automorphism of order 9

Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number we have classified all binary self-dual codes with length 76 having minimum distance $d=14$ and automorphism of order 9. Up to equivalence, there are six self-dual $[76, 38, 14]$ codes with an automorphism of type $9$-$(8,0,4)$. All codes obtained have new values of the parameter in their weight enumerator thus more than doubling the number of known values.

math.CO↗
arXiv2017

New extremal singly even self-dual codes of lengths $64$ and $66$

For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly even self-dual $[64,32,12]$ codes with covering radius $12$ meeting the Delsarte bound.

math.CO↗
arXiv2014

On the Automorphisms of Order 15 for a Binary Self-Dual [96, 48, 20] Code

The structure of binary self-dual codes invariant under the action of a cyclic group of order $pq$ for odd primes $p\neq q$ is considered. As an application we prove the nonexistence of an extremal self-dual $[96, 48, 20]$ code with an automorphism of order $15$ which closes a gap in `"On extremal self-dual codes of length 96", IEEE Trans. Inf. Theory, vol. 57, pp. 6820-6823, 2011'.

cs.IT↗
arXiv2012

Classification of Binary Self-Dual [48,24,10] Codes with an Automorphism of Odd Prime Order

The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c,f) with p being an odd prime, then p=3, c=16, f=0. By considering only an automorphism of type 3-(16,0), we prove that there are exactly 264 inequivalent self-dual [48, 24, 10] codes with an automorphism of odd prime order, equivalently, there are exactly 264 inequivalent cubic self-dual [48, 24, 10] codes.

cs.IT↗