Let C be a 1-perfect additive code. The extended code C? is an extended 1-perfect 4-linear or additive non 4-linear code. If C? is the extended 1-perfect additive non 4-linear code of C and we puncture a binary coordinate, then (C?)0 is isomorphic to C. We will prove that a punctured extended 4-linear code is not a 1-perfect additive code up to the extended Hamming code of length 16. Keywords:Perfect codes, extended codes, quaternary codes, additive codes, 4-linear codes.
We denote GF_4={0,1,w,w^2} where w^2=w+1. An additive code C over GF_4 of length n is an additive su...
linear codes C and C ′ of length n are (permutation)-equivalent if for some permutation σ of In = {1...
In this paper, we introduce additive Toeplitz codes over F4. The additive Toeplitz codes are a gene...
AbstractThe two 1-error correcting perfect binary codes, C and C′ are said to be equivalent if there...
A code C is Z₂Z₄-additive if the set of coordinates can be partitioned into two subsets X and Y such...
We study additive quaternary codes whose parameters are close to those of the extended cyclic $[{12,...
AbstractFor an [n,k,d]4 code C with d odd, we define the diversity of C as the 3-tuple (Φ0,Φ1,Φ2) wi...
When discussing equivalent codes, the literature tends to define equivalence differently for linear ...
A code is qm-ary q-linear if its alphabet forms an m-dimensional vector space over q and the code is...
A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been...
AbstractEvery linear code over GF(4) with odd minimum distance d is extendable if Ai=0 for all i≡2(m...
AbstractR. Hill and P. Lizak (1995, in “Proc. IEEE Int. Symposium on Inform. Theory, Whistler, Canad...
International audienceA linear code is linear complementary dual (LCD) if it meets its dual triviall...
RésuméA recent new construction of binary single error perfect codes is generalized over GF(q). Thes...
Abstract—A binary code is called Z4-linear if its quaternary Gray map preimage is linear. We show th...
We denote GF_4={0,1,w,w^2} where w^2=w+1. An additive code C over GF_4 of length n is an additive su...
linear codes C and C ′ of length n are (permutation)-equivalent if for some permutation σ of In = {1...
In this paper, we introduce additive Toeplitz codes over F4. The additive Toeplitz codes are a gene...
AbstractThe two 1-error correcting perfect binary codes, C and C′ are said to be equivalent if there...
A code C is Z₂Z₄-additive if the set of coordinates can be partitioned into two subsets X and Y such...
We study additive quaternary codes whose parameters are close to those of the extended cyclic $[{12,...
AbstractFor an [n,k,d]4 code C with d odd, we define the diversity of C as the 3-tuple (Φ0,Φ1,Φ2) wi...
When discussing equivalent codes, the literature tends to define equivalence differently for linear ...
A code is qm-ary q-linear if its alphabet forms an m-dimensional vector space over q and the code is...
A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been...
AbstractEvery linear code over GF(4) with odd minimum distance d is extendable if Ai=0 for all i≡2(m...
AbstractR. Hill and P. Lizak (1995, in “Proc. IEEE Int. Symposium on Inform. Theory, Whistler, Canad...
International audienceA linear code is linear complementary dual (LCD) if it meets its dual triviall...
RésuméA recent new construction of binary single error perfect codes is generalized over GF(q). Thes...
Abstract—A binary code is called Z4-linear if its quaternary Gray map preimage is linear. We show th...
We denote GF_4={0,1,w,w^2} where w^2=w+1. An additive code C over GF_4 of length n is an additive su...
linear codes C and C ′ of length n are (permutation)-equivalent if for some permutation σ of In = {1...
In this paper, we introduce additive Toeplitz codes over F4. The additive Toeplitz codes are a gene...