MASS FORMULA OF SELF-DUAL CODES OVER GALOIS RINGS GR(p<sup>2</sup>, 2)

Choi, Whan-Hyuk

doi:10.11568/kjm.2016.24.4.751

Cited by 4 publications

(2 citation statements)

References 10 publications

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“…But it is completely characterized by the triplet formed by these two codes and a map between the residue code and the cosets of the torsion code. This is similar to the technique used to derive mass formulas for self-dual codes over rings [2,5,9]. In Sect.…”

Section: Introductionmentioning

confidence: 93%

Quasi type IV codes over a non-unital ring

Alahmadi

Altassan

Basaffar

et al. 2021

AAECC

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There is a local ring I of order 4, without identity for the multiplication, defined by generators and relations asWe give a natural map between linear codes over I and additive codes over 4 , that allows for efficient computations. We study the algebraic structure of linear codes over this non-unital local ring, their generator and parity-check matrices. A canonical form for these matrices is given in the case of so-called nice codes. By analogy with ℤ 4 -codes, we define residue and torsion codes attached to a linear I-code. We introduce the notion of quasi self-dual codes (QSD) over I, and Type IV I-codes, that is, QSD codes all codewords of which have even Hamming weight. This is the natural analogue of Type IV codes over the field 4 . Further, we define quasi Type IV codes over I as those QSD codes with an even torsion code. We give a mass formula for QSD codes, and another for quasi Type IV codes, and classify both types of codes, up to coordinate permutation equivalence, in short lengths.

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Section: Introductionmentioning

confidence: 93%

Quasi type IV codes over a non-unital ring

Alahmadi

Altassan

Basaffar

et al. 2021

AAECC

View full text Add to dashboard Cite

show abstract

“…Mass formulas serve as important tools for classifying self-dual codes over finite fields [1][2][3][4][5] and unitary rings [6][7][8][9][10][11]. When generating nonequivalent self-dual codes, mass formulas serve as terminating flags for the computing effort.…”

Section: Introductionmentioning

confidence: 99%