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Every unit $u$ in the ring $\mathbf{Z}_{n}$ of the residual classes mod $n$ induces canonically an automorphism $\pi$ of the algebra $\mathbf{R}_{n}(q)=GF(q)[z]/(z^{n}-1)$ . Let $\mathcal{C}\subset\mathbf{R}_{n}(q)$ be a cyclic code, i.e. an ideal. If the numbers $n$ and $q$ are relatively prime then there exists a well-known characterization of the code $\pi(\mathcal{C})$ . We extend this characterization to the general case.

Maximal circular codes versus maximal codes

Yannick Guesnet (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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.

Maximal circular codes versus maximal codes

Yannick Guesnet (2010)

RAIRO - Theoretical Informatics and Applications

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.

Minimal Codewords in Linear Codes

Borissov, Yuri, Manev, Nickolai (2004)

Serdica Mathematical Journal

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...

On block irreducible forms over Euclidean domains.

Clark, W.Edwin, Liang, J.J. (1980)

International Journal of Mathematics and Mathematical Sciences

On codes with finite interpreting delay : a defect theorem

Yannick Guesnet (2000)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

On codes with finite interpreting delay: a defect theorem

Yannick Guesnet (2010)

RAIRO - Theoretical Informatics and Applications

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.

On the Weight Distribution of the Coset Leaders of Constacyclic Codes

Velikova, Evgeniya, Bojilov, Asen (2008)

Serdica Journal of Computing

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...

Perfect arithmetic codes

H. W., Jr. Lenstra (1977/1978)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Poids des duaux des codes BCH de distance prescrite $2^{a} + 1$ et sommes exponentielles

Éric Férard (2002)

Bulletin de la Société Mathématique de France

Soit $n$ un entier pair. On considère un code BCH binaire $C_{n}$ de longueur $2^{n} - 1$ et de distance prescrite $2^{a} + 1$ avec $a \geq 3$ . Le poids d’un mot non nul du dual de $C_{n}$ 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 $C_{n}$ .

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Balancing cyclic $R$ -ary Gray codes.

Balancing cyclic $R$ -ary Gray codes. II.

Codes correcteurs d'erreurs.

Completing codes

Construction of all maximal codes using MDS codes. (Die Konstruktion aller maximalen Code mit Hilfe von MDS-Coden.)

Évariste Galois et la planète Mars : introduction à la théorie algébrique du codage

Fast computation of Gauss sums and resolution of the root of unity ambiguity

Il teorema di equivalenza per i codici ciclici

Maximal circular codes versus maximal codes

Maximal circular codes versus maximal codes

Minimal Codewords in Linear Codes

On block irreducible forms over Euclidean domains.

On codes with finite interpreting delay : a defect theorem

On codes with finite interpreting delay: a defect theorem

On the Weight Distribution of the Coset Leaders of Constacyclic Codes

Perfect arithmetic codes

Poids des duaux des codes BCH de distance prescrite $2^{a} + 1$ et sommes exponentielles

Poids des duaux des codes BCH de distance prescrite $p^{a_{0}}$ et sommes exponentielles

О величине переноса в соседний разряд, возникающего в арифметических кодах

О проверочной матрице циклического кода, порожденного кратными корнями

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