Balancing cyclic -ary Gray codes.
Every unit in the ring of the residual classes mod induces canonically an automorphism of the algebra . Let be a cyclic code, i.e. an ideal. If the numbers and are relatively prime then there exists a well-known characterization of the code . We extend this characterization to the general case.
We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.
We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.
2000 Mathematics Subject Classification: 94B05, 94B15.Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in codes C and of weight 12 in their extended codes ^C are determined. The weight distributions of minimal codewords in the binary Reed-Muller codes RM (3, 6) and RM (3, 7) are determined. The applied method enables codes with larger parameters to...
We introduce two new classes of codes, namely adjacent codes and codes with finite interpreting delay. For each class, we establish an extension of the defect theorem.
Constacyclic codes with one and the same generator polynomial and distinct length are considered. We give a generalization of the previous result of the first author [4] for constacyclic codes. Suitable maps between vector spaces determined by the lengths of the codes are applied. It is proven that the weight distributions of the coset leaders don’t depend on the word length, but on generator polynomials only. In particular, we prove that every constacyclic code has the same weight distribution...
Soit un entier pair. On considère un code BCH binaire de longueur et de distance prescrite avec . Le poids d’un mot non nul du dual de peut s’exprimer en fonction d’une somme exponentielle. Nous montrerons que cette somme n’atteint pas la borne de Weil et nous proposerons une amélioration de celle-ci. En conséquence, nous obtiendrons une amélioration de la borne de Carlitz-Uchiyama sur le poids des mots du dual de .