Nikolay Yankov

• PhD, DSc
• Managing Director at Shumen University

In this work we apply the method for constructing binary LCD codes via an automorphism of prime order described in [3] and [4]. Thus we obtain all optimal LCD codes of lengths 26, 27 and 28 possessing an automorphism of order 13 with two cycles.

For lengths 60, 62, and 64, by applying the method for constructing self-dual codes having an automorphism of odd prime order, we classify all optimal singly even self-dual codes with an automorphism of order 5 with 12 cycles. For the binary self-dual [62, 31, 12] codes we have found five new values of the parameter in the weight enumerator thus do...

This paper studies and classifies optimal binary self-dual codes having an automorphism of order 7 with 9 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order p. There are exactly 69781 inequivalent binary self-dual [64,32,12] codes with an automorphism of type 7−(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...

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...

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.

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.

Using a method for constructing binary self-dual codes having an automorphism of odd prime order p we classify, up to equivalence, all singly-even self-dual [78, 39, 14], [80, 40, 14], [82, 41, 14], and [84, 42, 14] codes as well as all doubly-even [80, 40, 16] codes for p = 13. The results show that there are exactly 1592 inequivalent binary self-...

In this paper, we study optimal binary self-dual codes with minimum distance 12 having an automorphism of order 17. We prove that all such codes have parameters [68 + f, 34 + f/2, 12], f = 0, 2, 4 and an automorphism of type 17 − (4, f), f = 0, 2, 4 and provide a full classification of these codes. This classification gives new values β = 17, 153,...

We investigate binary self-dual [74, 37, 14] codes with an automorphism of type 7 − (10, 4) and we obtain some results for the structure of its automorphism group G. Eventually we prove that 49 do not divide the order of G. We calculate the possible weight enumerators for self-dual [74, 37, 12] codes and we construct examples of such codes for 292...

Using a method for constructing self-dual codes having an automorphism of odd prime order, we classify up to equivalence all binary self-dual codes with an automorphism of order 11 with 6 cycles and minimum distance 12. This classification gives new [72, 36, 12] codes with weight enumerator that was previously not obtained as well as many [66, 33,...

Using a method for constructing binary self-dual codes with an automorphism of odd prime order $p$ p , we give a full classification of all optimal binary self-dual $[50+2t,25+t]$ [ 50 + 2 t , 25 + t ] codes having an automorphism of order 5 for $t=0,\dots ,5$ t = 0 , ⋯ , 5 . As a consequence, we determine the weight enumerators for whi...

In this paper we study the self-dual codes of lengths 98 and 100 with minimum weight 18 invariant under a cyclic group of order 15. We prove that the putative self-dual [98, 49, 18] codes do not have automorphisms of order 15.

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,...

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. The...

This paper studies and classifies all binary self-dual [62,31,12] and [64,32,12] codes having an automorphism of order 7 with 8 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order p. There are exactly 8 inequivalent binary self-dual [62,31,12] codes with an automor...

A new method for constructing binary self-dual codes with an automorphism of order pq for p ≠ q was developed in [1]. We use this method to construct new doubly-even self-dual [96, 48, 16] codes having an automorphism of order 15 with 6 cycles of length 15 and two cycles of length 3. More than 100000 new such codes are obtain. We found exactly 219...

We classify up to equivalence all optimal binary self-dual [52, 26, 10] codes having an automorphism of order 3 with 10 fixed points. We achieve this using a method for constructing self-dual codes via an automorphism of odd prime order. We study also codes with an automorphism of order 3 with 4 fixed points. Some of the constructed codes have new...

By applying a method for constructing binary self-dual codes with an automorphism of odd prime order \(p\) , we give a full classification of all optimal binary self-dual codes of length 50 having an automorphism of order 3. As a consequence, we give a full classification of all \([50, 25, 10]\) codes possessing 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 the...

In this paper, we prove that there does not exist a binary self-dual doubly even $[72, 36, 16]$ code with an automorphism of order 9. To do so, we apply a method for constructing binary self-dual codes possessing an automorphism of order $p^2$ for an odd prime $p$.

All binary [ n , n /2] optimal self-dual codes for length 52 ≤ n ≤ 60 with an automorphism of order 7 or 13 are classified up to equivalence. Two of the constructed [54,27,10] codes have weight enumerators that were not previously known to exist. There are also some [58,29,10] codes with new values of the parameters in their weight enumerator.

All binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 are classified. In this way we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.

All binary self-dual [44, 22, 8], codes with an automorphism of order 3 or 7 are classified. In this way, we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.

All binary self-dual [44, 22, 8] codes with an automorphism of order 3 with 8, 10, and 12 independent cycles are classified up to equivalence. There exist exactly 4570 inequivalent codes with automorphism of order 3 with 8 independent cycles, 8738 inequivalent such codes with 10 cycles, and 123147 inequivalent codes with 12 cycles.

A method for constructing binary self-dual codes having an automorphism of order p 2 for an odd prime p is presented in (S. Bouyuklieva et al. IEEE. Trans. Inform. Theory, 51, 3678–3686, 2005). Using this method, we investigate the optimal self-dual codes of lengths 60 ≤ n ≤ 66 having an automorphism of order 9 with six 9-cycles, t cycles of length...

All optimal binary self-dual codes of length 42 which have an automorphism of order 3 are constructed. In this way we complete the classification of [42,21,8] SD codes having an automorphism of odd prime order.

We describe a method for constructing binary self-dual codes having an automorphism of order p² for an odd prime p. Using this method, we classify the optimal self-dual codes of lengths 36 ≤ n ≤ 44 and n = 54, having an automorphism of order 9. We obtain all self-dual (56,28,12),(58,29,10), and (60,30,12) codes having an automorphism of...