Almost all self-dual codes are rigid

Almost All Palindromes Are Composite

We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x as x → ∞. Our results show that almost all palindromes in a given base are composite. ∗MSC Numbers: 11A63, 11L07, 11N69 †Corresponding author 1

Extremal self-dual codes

In the present thesis we consider extremal self-dual codes. We mainly concentrate on Type II codes (binary doubly-even codes), which may theoretically exist for lengths n = 8k ≤ 3928. It is noteworthy that extremal Type II codes have been actually constructed only for 13 lengths, 136 being the largest. Over the last decades the study of extremal codes became inseparable from the study of their ...

Self-Dual Codes

Cyclic self-dual codes

Ahstruct-It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial code in this class is shown to hav...

Self-Dual Codes

A survey of self-dual codes, written for the Handbook of Coding Theory. Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this chapter include codes over