Self-Orthogonality Matrix and Reed-Muller Codes

Kim, Jon-Lark; Choi, Whan-Hyuk

doi:10.1109/tit.2022.3186316

Cited by 7 publications

(21 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kim and Choi propose two conjectures in [14]. In this subsection, we prove the conjectures using the above method.…”

Section: Two Conjectures On Binary Optimal [N 5] Self-orthogonal Codesmentioning

confidence: 97%

“…But the converse may not be true. For example, there exists a binary [45, 5, 22] SO code [14], but there are no binary [14,5,6] SO codes [5]. In fact, the result holds when 2d−n ≥ 0 (see Lemma 3.6 in [1]).…”

Section: Binary So Codes Related To the Simplex Codesmentioning

confidence: 99%

“…In order to solve Conjecture 20 in [14], we introduce an interesting and useful lemma, which was proved in [ That is to say, d so (n, 5) = d(n, 5) − 2 for n ≥ 32 and n ≡ 6, 13, 21, 28 (mod 31). This completes the proof.…”

Section: Two Conjectures On Binary Optimal [N 5] Self-orthogonal Codesmentioning

confidence: 99%

“…Recently, Kim and Choi [14] constructed many new optimal binary SO codes of dimensions 5 and 6 and gave two conjectures. In this paper, we consider the next step of [5,13,14,16].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Kim and Choi [14] constructed many new optimal binary SO codes of dimensions 5 and 6 and gave two conjectures. In this paper, we consider the next step of [5,13,14,16]. Using binary SO codes related to the simplex codes, we determine the exact values of d so (n, 5) and d so (n, 6), which solves the two conjectures proposed by Kim and Choi [14], and furthermore completely generalize some results of the paper.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5

Shi¹,

Li²,

Kim³

2022

Preprint

View full text Add to dashboard Cite

The purpose of this paper is to solve the two conjectures on the largest minimum distance d so (n, 5) of a binary self-orthogonal [n, 5] code proposed by Kim and Choi (IEEE Trans. Inf. Theory, 2022). The determination of d so (n, k) has been a fundamental and difficult problem in coding theory because there are too many binary self-orthogonal codes as the dimension k increases. Recently, Kim et al. ( 2021) considered the shortest self-orthogonal embedding of a binary linear code, and many binary optimal self-orthogonal [n, k] codes were constructed for k = 4, 5. Kim and Choi (2022) improved some results of Kim et al. ( 2021) and made two conjectures on d so (n, 5). In this paper, we develop a general method to determine the exact value of d so (n, k) for k = 5, 6 and show that the two conjectures made by Kim and Choi (2022) are true.

show abstract

“…Kim and Choi propose two conjectures in [14]. In this subsection, we prove the conjectures using the above method.…”

Section: Two Conjectures On Binary Optimal [N 5] Self-orthogonal Codesmentioning

confidence: 97%

Section: Binary So Codes Related To the Simplex Codesmentioning

confidence: 99%

Section: Two Conjectures On Binary Optimal [N 5] Self-orthogonal Codesmentioning

confidence: 99%

“…Recently, Kim and Choi [14] constructed many new optimal binary SO codes of dimensions 5 and 6 and gave two conjectures. In this paper, we consider the next step of [5,13,14,16].…”

Section: Introductionmentioning

confidence: 99%