CONSTRUCTION OF SELF-DUAL CODES OVER F<sub>2</sub>+ uF<sub>2</sub>

Han, Sunghyu; Lee, Heisook; Lee, Yoonjin

doi:10.4134/bkms.2012.49.1.135

Cited by 18 publications

(19 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The build-up method is a powerful technique to construct self-dual codes over fields and rings [7,10]. Starting from a self-dual code of length n, it builds a self-dual code of length n + 2 by a simple recursion.…”

Section: Introductionmentioning

confidence: 99%

The build-up construction of quasi self-dual codes over a non-unital ring

et al. 2021

View full text Add to dashboard Cite

There is a local ring [Formula: see text] of order [Formula: see text] without identity for the multiplication, defined by generators and relations as [Formula: see text] We study a recursive construction of self-orthogonal codes over [Formula: see text] We classify, up to permutation equivalence, self-orthogonal codes of length [Formula: see text] and size [Formula: see text] (called here quasi self-dual codes or QSD) up to the length [Formula: see text]. In particular, we classify Type IV codes (QSD codes with even weights) up to [Formula: see text].

show abstract

Section: Introductionmentioning

confidence: 99%

The build-up construction of quasi self-dual codes over a non-unital ring

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Using this idea, many good self-dual codes over F 2 m for various positive integers m have been constructed from self-dual codes over F 2 m + uF 2 m (cf. [9], [24], [25], [38], [5], [30], [31], [35]- [37]).…”

Section: Introductionmentioning

confidence: 99%

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u ^2λ›

et al. 2020

View full text Add to dashboard Cite

Let F 2 m be a finite field of 2 m elements, λ and k be integers satisfying λ, k ≥ 2 and denote R = F 2 m [u]/ u 2λ. Let δ, α ∈ F × 2 m. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ + αu 2)-constacyclic codes over R of length 2 k n, and provide a clear formula to count the number of all these codes. In particular, we conclude that every (δ + αu 2)-constacyclic code over R of length 2 k n is an ideal generated by at most 2 polynomials in the ring R[x]/ x 2 k n − (δ + αu 2). As an example, we listed all 135 distinct (1 + u 2)-constacyclic codes of length 4 over F 2 [u] u 4 , and apply our results to determine all 11 self-dual codes among them. INDEX TERMS Type 2 constacyclic code, linear code, repeated-root code, finite chain ring.

show abstract

“…There were many literatures on the construction of binary self-dual codes from various kind of codes over F 2 m + uF 2 m for m = 1, 2. For some of these constructions, we refer to [10], [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On self-duality and hulls of cyclic codes over $$\frac{\mathbb {F}_{2^m}[u]}{\langle u^k\rangle }$$ with oddly even length

Cao

Chen

2019

AAECC

View full text Add to dashboard Cite

Let F 2 m be a finite field of 2 m elements, andFor any odd positive integer n, an explicit representation for every self-dual cyclic code over R of length 2n and a mass formula to count the number of these codes are given first. Then a generator matrix is provided for the selfdual and 2-quasi-cyclic code of length 4n over F 2 m derived by every self-dual cyclic code of length 2n over F 2 m + uF 2 m and a Gray map from F 2 m + uF 2 m onto F 2 2 m . Finally, the hull of each cyclic code with length 2n over F 2 m + uF 2 m is determined and all distinct self-orthogonal cyclic codes of length 2n over F 2 m + uF 2 m are listed.On self-duality and hulls of cyclic codes overu k with oddly even length 3On self-duality and hulls of cyclic codes overwith oddly even length 5On self-duality and hulls of cyclic codes over F 2 m [u] u k with oddly even length 9

show abstract

CONSTRUCTION OF SELF-DUAL CODES OVER F₂+ uF₂

Cited by 18 publications

References 7 publications

The build-up construction of quasi self-dual codes over a non-unital ring

The build-up construction of quasi self-dual codes over a non-unital ring

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u ^2λ›

On self-duality and hulls of cyclic codes over $$\frac{\mathbb {F}_{2^m}[u]}{\langle u^k\rangle }$$ with oddly even length

Contact Info

Product

Resources

About

CONSTRUCTION OF SELF-DUAL CODES OVER F2+ uF2

Cited by 18 publications

References 7 publications

The build-up construction of quasi self-dual codes over a non-unital ring

The build-up construction of quasi self-dual codes over a non-unital ring

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂ m [u]/‹u 2λ›

On self-duality and hulls of cyclic codes over $$\frac{\mathbb {F}_{2^m}[u]}{\langle u^k\rangle }$$ with oddly even length

Contact Info

Product

Resources

About

CONSTRUCTION OF SELF-DUAL CODES OVER F₂+ uF₂

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u ^2λ›